LMFDB - Embedded newform 483.2.bf.a.178.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(10,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 11, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bf (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$32$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			178.18
Character	$\chi$	$=$	483.178
Dual form			483.2.bf.a.19.18

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.177076 - 0.0169087i) q^{2} +(-0.690079 - 0.723734i) q^{3} +(-1.93279 + 0.372514i) q^{4} +(1.69892 + 0.875853i) q^{5} +(-0.134434 - 0.116488i) q^{6} +(-2.13977 - 1.55608i) q^{7} +(-0.677305 + 0.198875i) q^{8} +(-0.0475819 + 0.998867i) q^{9} +O(q^{10})$	\(q+(0.177076 - 0.0169087i) q^{2} +(-0.690079 - 0.723734i) q^{3} +(-1.93279 + 0.372514i) q^{4} +(1.69892 + 0.875853i) q^{5} +(-0.134434 - 0.116488i) q^{6} +(-2.13977 - 1.55608i) q^{7} +(-0.677305 + 0.198875i) q^{8} +(-0.0475819 + 0.998867i) q^{9} +(0.315648 + 0.126366i) q^{10} +(-0.305519 + 3.19954i) q^{11} +(1.60338 + 1.14176i) q^{12} +(3.50608 - 0.504098i) q^{13} +(-0.405214 - 0.239363i) q^{14} +(-0.538503 - 1.83397i) q^{15} +(3.53815 - 1.41646i) q^{16} +(1.88112 + 5.43513i) q^{17} +(0.00846395 + 0.177680i) q^{18} +(-2.64533 + 7.64319i) q^{19} +(-3.60991 - 1.05997i) q^{20} +(0.350428 + 2.62244i) q^{21} +0.571728i q^{22} +(4.74465 - 0.698774i) q^{23} +(0.611326 + 0.352949i) q^{24} +(-0.781083 - 1.09688i) q^{25} +(0.612320 - 0.148547i) q^{26} +(0.755750 - 0.654861i) q^{27} +(4.71539 + 2.21047i) q^{28} +(-4.25192 + 4.90698i) q^{29} +(-0.126366 - 0.315648i) q^{30} +(-4.23404 - 1.02717i) q^{31} +(1.85743 - 0.957570i) q^{32} +(2.52645 - 1.98682i) q^{33} +(0.425003 + 0.930626i) q^{34} +(-2.27240 - 4.51777i) q^{35} +(-0.280127 - 1.94832i) q^{36} +(8.47795 + 0.403854i) q^{37} +(-0.339189 + 1.39816i) q^{38} +(-2.78430 - 2.18960i) q^{39} +(-1.32487 - 0.255348i) q^{40} +(1.14661 + 1.78417i) q^{41} +(0.106395 + 0.458447i) q^{42} +(-3.46130 + 11.7881i) q^{43} +(-0.601370 - 6.29784i) q^{44} +(-0.955698 + 1.65532i) q^{45} +(0.828350 - 0.203962i) q^{46} +(3.29504 - 1.90239i) q^{47} +(-3.46674 - 1.58321i) q^{48} +(2.15726 + 6.65930i) q^{49} +(-0.156858 - 0.181024i) q^{50} +(2.63547 - 5.11210i) q^{51} +(-6.58872 + 2.28038i) q^{52} +(1.01011 - 1.28445i) q^{53} +(0.122752 - 0.128739i) q^{54} +(-3.32138 + 5.16816i) q^{55} +(1.75874 + 0.628391i) q^{56} +(7.35713 - 3.35989i) q^{57} +(-0.669944 + 0.940805i) q^{58} +(2.71467 - 6.78093i) q^{59} +(1.72399 + 3.34408i) q^{60} +(1.46781 + 1.39955i) q^{61} +(-0.767116 - 0.110295i) q^{62} +(1.65613 - 2.06331i) q^{63} +(-6.09957 + 3.91996i) q^{64} +(6.39805 + 2.21439i) q^{65} +(0.413779 - 0.394538i) q^{66} +(-7.16923 + 5.10519i) q^{67} +(-5.66046 - 9.80421i) q^{68} +(-3.77991 - 2.95166i) q^{69} +(-0.478779 - 0.761566i) q^{70} +(4.66441 - 10.2136i) q^{71} +(-0.166422 - 0.686000i) q^{72} +(-0.886843 - 4.60138i) q^{73} +(1.50807 - 0.0718383i) q^{74} +(-0.254839 + 1.32223i) q^{75} +(2.26567 - 15.7581i) q^{76} +(5.63246 - 6.37088i) q^{77} +(-0.530057 - 0.340647i) q^{78} +(-2.97716 - 3.78577i) q^{79} +(7.25163 + 0.692447i) q^{80} +(-0.995472 - 0.0950560i) q^{81} +(0.233206 + 0.296546i) q^{82} +(-12.8156 - 8.23609i) q^{83} +(-1.65420 - 4.93808i) q^{84} +(-1.56451 + 10.8814i) q^{85} +(-0.413592 + 2.14592i) q^{86} +(6.48551 - 0.308943i) q^{87} +(-0.429377 - 2.22782i) q^{88} +(-1.33103 - 5.48657i) q^{89} +(-0.141242 + 0.309277i) q^{90} +(-8.28662 - 4.37707i) q^{91} +(-8.91010 + 3.11803i) q^{92} +(2.17843 + 3.77314i) q^{93} +(0.551307 - 0.392584i) q^{94} +(-11.1885 + 10.6682i) q^{95} +(-1.97480 - 0.683484i) q^{96} +(-8.72838 + 5.60939i) q^{97} +(0.494600 + 1.14273i) q^{98} +(-3.18138 - 0.457413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	$ 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) $ 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.177076	−	0.0169087i	0.125212	−	0.0119563i	−0.0322619	−	0.999479i	$-0.510271\pi$
$2$	0.177076	−	0.0169087i	0.125212	−	0.0119563i	0.157474	+	0.987523i	$0.449665\pi$
$3$	−0.690079	−	0.723734i	−0.398417	−	0.417848i
$3$	−0.690079	−	0.723734i	−0.398417	−	0.417848i
$4$	−1.93279	+	0.372514i	−0.966394	+	0.186257i
$5$	1.69892	+	0.875853i	0.759779	+	0.391693i	0.794155	−	0.607716i	$-0.207914\pi$
$5$	1.69892	+	0.875853i	0.759779	+	0.391693i	−0.0343758	+	0.999409i	$0.510944\pi$
$6$	−0.134434	−	0.116488i	−0.0548825	−	0.0475559i
$7$	−2.13977	−	1.55608i	−0.808758	−	0.588141i
$7$	−2.13977	−	1.55608i	−0.808758	−	0.588141i
$8$	−0.677305	+	0.198875i	−0.239463	+	0.0703128i
$9$	−0.0475819	+	0.998867i	−0.0158606	+	0.332956i
$10$	0.315648	+	0.126366i	0.0998165	+	0.0399605i
$11$	−0.305519	+	3.19954i	−0.0921174	+	0.964697i	0.824748	+	0.565500i	$0.191317\pi$
$11$	−0.305519	+	3.19954i	−0.0921174	+	0.964697i	−0.916865	+	0.399197i	$0.869289\pi$
$12$	1.60338	+	1.14176i	0.462855	+	0.329598i
$13$	3.50608	−	0.504098i	0.972411	−	0.139812i	0.362243	−	0.932084i	$-0.382011\pi$
$13$	3.50608	−	0.504098i	0.972411	−	0.139812i	0.610168	+	0.792272i	$0.291102\pi$
$14$	−0.405214	−	0.239363i	−0.108298	−	0.0639725i
$15$	−0.538503	−	1.83397i	−0.139041	−	0.473529i
$16$	3.53815	−	1.41646i	0.884537	−	0.354115i
$17$	1.88112	+	5.43513i	0.456238	+	1.31821i	0.905323	+	0.424724i	$0.139629\pi$
$17$	1.88112	+	5.43513i	0.456238	+	1.31821i	−0.449085	+	0.893489i	$0.648250\pi$
$18$	0.00846395	+	0.177680i	0.00199497	+	0.0418796i
$19$	−2.64533	+	7.64319i	−0.606881	+	1.75347i	0.0492111	+	0.998788i	$0.484329\pi$
$19$	−2.64533	+	7.64319i	−0.606881	+	1.75347i	−0.656093	+	0.754680i	$0.727792\pi$
$20$	−3.60991	−	1.05997i	−0.807201	−	0.237016i
$21$	0.350428	+	2.62244i	0.0764696	+	0.572264i
$22$			0.571728i			0.121893i
$23$	4.74465	−	0.698774i	0.989328	−	0.145704i
$23$	4.74465	−	0.698774i	0.989328	−	0.145704i
$24$	0.611326	+	0.352949i	0.124786	+	0.0720455i
$25$	−0.781083	−	1.09688i	−0.156217	−	0.219376i
$26$	0.612320	−	0.148547i	0.120086	−	0.0291325i
$27$	0.755750	−	0.654861i	0.145444	−	0.126028i
$28$	4.71539	+	2.21047i	0.891124	+	0.417739i
$29$	−4.25192	+	4.90698i	−0.789562	+	0.911203i	−0.997761	−	0.0668831i	$-0.978695\pi$
$29$	−4.25192	+	4.90698i	−0.789562	+	0.911203i	0.208198	+	0.978087i	$0.433240\pi$
$30$	−0.126366	−	0.315648i	−0.0230712	−	0.0576291i
$31$	−4.23404	−	1.02717i	−0.760456	−	0.184485i	−0.163263	−	0.986583i	$-0.552202\pi$
$31$	−4.23404	−	1.02717i	−0.760456	−	0.184485i	−0.597193	+	0.802098i	$0.703717\pi$
$32$	1.85743	−	0.957570i	0.328350	−	0.169276i
$33$	2.52645	−	1.98682i	0.439798	−	0.345861i
$34$	0.425003	+	0.930626i	0.0728873	+	0.159601i
$35$	−2.27240	−	4.51777i	−0.384106	−	0.763642i
$36$	−0.280127	−	1.94832i	−0.0466878	−	0.324721i
$37$	8.47795	+	0.403854i	1.39377	+	0.0663932i	0.730971	−	0.682408i	$-0.239067\pi$
$37$	8.47795	+	0.403854i	1.39377	+	0.0663932i	0.662794	+	0.748801i	$0.269370\pi$
$38$	−0.339189	+	1.39816i	−0.0550238	+	0.226811i
$39$	−2.78430	−	2.18960i	−0.445845	−	0.350617i
$40$	−1.32487	−	0.255348i	−0.209480	−	0.0403740i
$41$	1.14661	+	1.78417i	0.179071	+	0.278640i	0.919172	−	0.393855i	$-0.128859\pi$
$41$	1.14661	+	1.78417i	0.179071	+	0.278640i	−0.740101	+	0.672495i	$0.765222\pi$
$42$	0.106395	+	0.458447i	0.0164170	+	0.0707399i
$43$	−3.46130	+	11.7881i	−0.527843	+	1.79767i	0.0718244	+	0.997417i	$0.477118\pi$
$43$	−3.46130	+	11.7881i	−0.527843	+	1.79767i	−0.599667	+	0.800250i	$0.704700\pi$
$44$	−0.601370	−	6.29784i	−0.0906600	−	0.949435i
$45$	−0.955698	+	1.65532i	−0.142467	+	0.246760i
$46$	0.828350	−	0.203962i	0.122134	−	0.0300726i
$47$	3.29504	−	1.90239i	0.480632	−	0.277493i	−0.240048	−	0.970761i	$-0.577163\pi$
$47$	3.29504	−	1.90239i	0.480632	−	0.277493i	0.720680	+	0.693268i	$0.243830\pi$
$48$	−3.46674	−	1.58321i	−0.500381	−	0.228517i
$49$	2.15726	+	6.65930i	0.308180	+	0.951328i
$50$	−0.156858	−	0.181024i	−0.0221831	−	0.0256006i
$51$	2.63547	−	5.11210i	0.369040	−	0.715837i
$52$	−6.58872	+	2.28038i	−0.913691	+	0.316231i
$53$	1.01011	−	1.28445i	0.138749	−	0.176433i	−0.711713	−	0.702470i	$-0.752080\pi$
$53$	1.01011	−	1.28445i	0.138749	−	0.176433i	0.850462	+	0.526037i	$0.176323\pi$
$54$	0.122752	−	0.128739i	0.0167045	−	0.0175192i
$55$	−3.32138	+	5.16816i	−0.447854	+	0.696875i
$56$	1.75874	+	0.628391i	0.235022	+	0.0839722i
$57$	7.35713	−	3.35989i	0.974476	−	0.445028i
$58$	−0.669944	+	0.940805i	−0.0879680	+	0.123534i
$59$	2.71467	−	6.78093i	0.353420	−	0.882801i	−0.640010	−	0.768366i	$-0.721070\pi$
$59$	2.71467	−	6.78093i	0.353420	−	0.882801i	0.993431	−	0.114435i	$-0.0365058\pi$
$60$	1.72399	+	3.34408i	0.222566	+	0.431719i
$61$	1.46781	+	1.39955i	0.187934	+	0.179194i	0.778205	−	0.628011i	$-0.216131\pi$
$61$	1.46781	+	1.39955i	0.187934	+	0.179194i	−0.590271	+	0.807205i	$0.700979\pi$
$62$	−0.767116	−	0.110295i	−0.0974238	−	0.0140074i
$63$	1.65613	−	2.06331i	0.208652	−	0.259952i
$64$	−6.09957	+	3.91996i	−0.762446	+	0.489995i
$65$	6.39805	+	2.21439i	0.793581	+	0.274661i
$66$	0.413779	−	0.394538i	0.0509327	−	0.0485642i
$67$	−7.16923	+	5.10519i	−0.875861	+	0.623698i	−0.927028	−	0.374992i	$-0.877645\pi$
$67$	−7.16923	+	5.10519i	−0.875861	+	0.623698i	0.0511667	+	0.998690i	$0.483706\pi$
$68$	−5.66046	−	9.80421i	−0.686432	−	1.18894i
$69$	−3.77991	−	2.95166i	−0.455048	−	0.355338i
$70$	−0.478779	−	0.761566i	−0.0572250	−	0.0910246i
$71$	4.66441	−	10.2136i	0.553563	−	1.21213i	−0.401534	−	0.915844i	$-0.631523\pi$
$71$	4.66441	−	10.2136i	0.553563	−	1.21213i	0.955098	−	0.296291i	$-0.0957498\pi$
$72$	−0.166422	−	0.686000i	−0.0196130	−	0.0808459i
$73$	−0.886843	−	4.60138i	−0.103797	−	0.538551i	−0.996184	−	0.0872794i	$-0.972183\pi$
$73$	−0.886843	−	4.60138i	−0.103797	−	0.538551i	0.892387	−	0.451271i	$-0.149029\pi$
$74$	1.50807	−	0.0718383i	0.175310	−	0.00835104i
$75$	−0.254839	+	1.32223i	−0.0294262	+	0.152678i
$76$	2.26567	−	15.7581i	0.259890	−	1.80758i
$77$	5.63246	−	6.37088i	0.641879	−	0.726029i
$78$	−0.530057	−	0.340647i	−0.0600172	−	0.0385707i
$79$	−2.97716	−	3.78577i	−0.334957	−	0.425932i	0.589175	−	0.808005i	$-0.299453\pi$
$79$	−2.97716	−	3.78577i	−0.334957	−	0.425932i	−0.924132	+	0.382073i	$0.875210\pi$
$80$	7.25163	+	0.692447i	0.810757	+	0.0774179i
$81$	−0.995472	−	0.0950560i	−0.110608	−	0.0105618i
$82$	0.233206	+	0.296546i	0.0257533	+	0.0327480i
$83$	−12.8156	−	8.23609i	−1.40670	−	0.904029i	−0.406741	−	0.913543i	$-0.633335\pi$
$83$	−12.8156	−	8.23609i	−1.40670	−	0.904029i	−0.999955	+	0.00951490i	$0.996971\pi$
$84$	−1.65420	−	4.93808i	−0.180488	−	0.538789i
$85$	−1.56451	+	10.8814i	−0.169695	+	1.18026i
$86$	−0.413592	+	2.14592i	−0.0445987	+	0.231400i
$87$	6.48551	−	0.308943i	0.695320	−	0.0331222i
$88$	−0.429377	−	2.22782i	−0.0457718	−	0.237487i
$89$	−1.33103	−	5.48657i	−0.141089	−	0.581575i	−0.997831	−	0.0658303i	$-0.979030\pi$
$89$	−1.33103	−	5.48657i	−0.141089	−	0.581575i	0.856742	−	0.515745i	$-0.172485\pi$
$90$	−0.141242	+	0.309277i	−0.0148882	+	0.0326007i
$91$	−8.28662	−	4.37707i	−0.868674	−	0.458841i
$92$	−8.91010	+	3.11803i	−0.928942	+	0.325077i
$93$	2.17843	+	3.77314i	0.225892	+	0.391257i
$94$	0.551307	−	0.392584i	0.0568630	−	0.0404920i
$95$	−11.1885	+	10.6682i	−1.14792	+	1.09454i
$96$	−1.97480	−	0.683484i	−0.201552	−	0.0697578i
$97$	−8.72838	+	5.60939i	−0.886232	+	0.569547i	−0.902677	−	0.430318i	$-0.858401\pi$
$97$	−8.72838	+	5.60939i	−0.886232	+	0.569547i	0.0164452	+	0.999865i	$0.494765\pi$
$98$	0.494600	+	1.14273i	0.0499621	+	0.115433i
$99$	−3.18138	−	0.457413i	−0.319740	−	0.0459717i
$100$	1.91827	+	1.82907i	0.191827	+	0.182907i
$101$	−5.61154	−	10.8849i	−0.558369	−	1.08309i	−0.983997	−	0.178187i	$-0.942977\pi$
$101$	−5.61154	−	10.8849i	−0.558369	−	1.08309i	0.425627	−	0.904898i	$-0.360053\pi$
$102$	0.380240	−	0.949794i	0.0376494	−	0.0940436i
$103$	4.63844	−	6.51378i	0.457039	−	0.641821i	−0.520180	−	0.854057i	$-0.674135\pi$
$103$	4.63844	−	6.51378i	0.457039	−	0.641821i	0.977219	+	0.212236i	$0.0680744\pi$
$104$	−2.27443	+	1.03870i	−0.223026	+	0.101853i
$105$	−1.70152	+	4.76223i	−0.166052	+	0.464746i
$106$	0.157147	−	0.244526i	0.0152635	−	0.0237505i
$107$	−12.6097	+	13.2247i	−1.21903	+	1.27848i	−0.270152	+	0.962818i	$0.587074\pi$
$107$	−12.6097	+	13.2247i	−1.21903	+	1.27848i	−0.948873	+	0.315659i	$0.897774\pi$
$108$	−1.21676	+	1.54723i	−0.117083	+	0.148883i
$109$	−1.56669	+	0.542237i	−0.150062	+	0.0519369i	−0.401066	−	0.916049i	$-0.631360\pi$
$109$	−1.56669	+	0.542237i	−0.150062	+	0.0519369i	0.251005	+	0.967986i	$0.419239\pi$
$110$	−0.500750	+	0.971319i	−0.0477446	+	0.0926116i
$111$	−5.55817	−	6.41447i	−0.527558	−	0.608835i
$112$	−9.77496	−	2.47472i	−0.923647	−	0.233839i
$113$	14.3623	+	6.55902i	1.35109	+	0.617021i	0.953736	−	0.300645i	$-0.0972020\pi$
$113$	14.3623	+	6.55902i	1.35109	+	0.617021i	0.397352	+	0.917666i	$0.369929\pi$
$114$	1.24596	−	0.719356i	0.116695	−	0.0673739i
$115$	8.67279	+	2.96846i	0.808742	+	0.276810i
$116$	6.39014	−	11.0681i	0.593310	−	1.02764i
$117$	0.336701	+	3.52609i	0.0311280	+	0.325987i
$118$	0.366047	−	1.24664i	0.0336974	−	0.114763i
$119$	4.43231	−	14.5571i	0.406309	−	1.33445i
$120$	0.729461	+	1.13506i	0.0665904	+	0.103617i
$121$	0.657513	+	0.126725i	0.0597739	+	0.0115205i
$122$	0.283579	+	0.223009i	0.0256740	+	0.0201903i
$123$	0.500008	−	2.06106i	0.0450842	−	0.185840i
$124$	8.56613	+	0.408055i	0.769261	+	0.0366444i
$125$	−1.72639	−	12.0073i	−0.154413	−	1.07397i
$126$	0.258373	−	0.393366i	0.0230177	−	0.0350438i
$127$	−1.95929	−	4.29024i	−0.173859	−	0.380698i	0.802564	−	0.596567i	$-0.203469\pi$
$127$	−1.95929	−	4.29024i	−0.173859	−	0.380698i	−0.976422	+	0.215869i	$0.930742\pi$
$128$	−4.29909	+	3.38084i	−0.379989	+	0.298827i
$129$	10.9200	−	5.62966i	0.961453	−	0.495664i
$130$	1.17039	+	0.283932i	0.102650	+	0.0249025i
$131$	4.13980	+	10.3407i	0.361696	+	0.903474i	0.991897	+	0.127042i	$0.0405482\pi$
$131$	4.13980	+	10.3407i	0.361696	+	0.903474i	−0.630201	+	0.776432i	$0.717028\pi$
$132$	−4.14297	+	4.78124i	−0.360599	+	0.416153i
$133$	17.5538	−	12.2384i	1.52211	−	1.06120i
$134$	−1.18318	+	1.02523i	−0.102211	+	0.0885664i
$135$	1.85752	−	0.450629i	0.159870	−	0.0387840i
$136$	−2.35500	−	3.30713i	−0.201940	−	0.283584i
$137$	15.1417	+	8.74208i	1.29365	+	0.746886i	0.979298	−	0.202422i	$-0.0648812\pi$
$137$	15.1417	+	8.74208i	1.29365	+	0.746886i	0.314347	+	0.949308i	$0.398215\pi$
$138$	−0.719241	−	0.458755i	−0.0612259	−	0.0390518i
$139$			12.6525i			1.07317i	0.843847	+	0.536584i	$0.180286\pi$
$139$			12.6525i			1.07317i	−0.843847	+	0.536584i	$0.819714\pi$
$140$	6.07501	+	7.88538i	0.513432	+	0.666437i
$141$	−3.65067	−	1.07193i	−0.307442	−	0.0902731i
$142$	0.653257	−	1.88746i	0.0548201	−	0.158392i
$143$	0.541708	+	11.3718i	0.0452999	+	0.950961i
$144$	1.24650	+	3.60154i	0.103875	+	0.300128i
$145$	−11.5215	+	4.61250i	−0.956805	+	0.383047i
$146$	−0.234842	−	0.799800i	−0.0194357	−	0.0661919i
$147$	3.33088	−	6.15672i	0.274726	−	0.507798i
$148$	−16.5365	+	2.37759i	−1.35929	+	0.195437i
$149$	12.6802	+	9.02953i	1.03880	+	0.739728i	0.966242	−	0.257636i	$-0.0829436\pi$
$149$	12.6802	+	9.02953i	1.03880	+	0.739728i	0.0725603	+	0.997364i	$0.476883\pi$
$150$	−0.0227687	+	0.238444i	−0.00185905	+	0.0194689i
$151$	10.4857	+	4.19783i	0.853313	+	0.341615i	0.756744	−	0.653711i	$-0.226789\pi$
$151$	10.4857	+	4.19783i	0.853313	+	0.341615i	0.0965689	+	0.995326i	$0.469213\pi$
$152$	0.271661	−	5.70286i	0.0220346	−	0.462563i
$153$	−5.51848	+	1.62037i	−0.446143	+	0.130999i
$154$	0.889652	−	1.22337i	0.0716902	−	0.0985819i
$155$	−6.29364	−	5.45347i	−0.505517	−	0.438033i
$156$	6.19712	+	3.19484i	0.496167	+	0.255792i
$157$	−12.1164	+	2.33525i	−0.966995	+	0.186373i	−0.648216	−	0.761456i	$-0.724485\pi$
$157$	−12.1164	+	2.33525i	−0.966995	+	0.186373i	−0.318778	+	0.947829i	$0.603273\pi$
$158$	−0.591198	−	0.620030i	−0.0470332	−	0.0493269i
$159$	−1.62666	+	0.155327i	−0.129002	+	0.0123182i
$160$	3.99430			0.315778
$161$	−11.2398	−	5.88782i	−0.885822	−	0.464025i
$162$	−0.177882			−0.0139757
$163$	20.7914	−	1.98534i	1.62851	−	0.155504i	0.759571	−	0.650425i	$-0.225409\pi$
$163$	20.7914	−	1.98534i	1.62851	−	0.155504i	0.868938	+	0.494921i	$0.164803\pi$
$164$	−2.88079	−	3.02129i	−0.224952	−	0.235923i
$165$	6.03239	−	1.16265i	0.469621	−	0.0905119i
$166$	−2.40860	−	1.24172i	−0.186944	−	0.0963762i
$167$	1.85763	+	1.60964i	0.143748	+	0.124558i	0.723766	−	0.690045i	$-0.242409\pi$
$167$	1.85763	+	1.60964i	0.143748	+	0.124558i	−0.580019	+	0.814603i	$0.696955\pi$
$168$	−0.758883	−	1.70650i	−0.0585491	−	0.131659i
$169$	−0.434943	+	0.127711i	−0.0334572	+	0.00982391i
$170$	−0.0930469	+	1.95330i	−0.00713637	+	0.149811i
$171$	−7.50867	−	3.00602i	−0.574202	−	0.229876i
$172$	2.29872	−	24.0733i	0.175276	−	1.83557i
$173$	−10.6802	−	7.60536i	−0.812004	−	0.578225i	0.0968699	−	0.995297i	$-0.469117\pi$
$173$	−10.6802	−	7.60536i	−0.812004	−	0.578225i	−0.908873	+	0.417072i	$0.863056\pi$
$174$	1.14321	−	0.164368i	0.0866663	−	0.0124607i
$175$	−0.0354840	+	3.56249i	−0.00268234	+	0.269299i
$176$	3.45105	+	11.7532i	0.260133	+	0.885931i
$177$	−6.78093	+	2.71467i	−0.509686	+	0.204047i
$178$	−0.328464	−	0.949035i	−0.0246194	−	0.0711332i
$179$	0.326661	+	6.85747i	0.0244158	+	0.512551i	0.977640	+	0.210286i	$0.0674396\pi$
$179$	0.326661	+	6.85747i	0.0244158	+	0.512551i	−0.953224	+	0.302265i	$0.902257\pi$
$180$	1.23053	−	3.55539i	0.0917184	−	0.265003i
$181$	11.0253	+	3.23733i	0.819506	+	0.240629i	0.664503	−	0.747285i	$-0.268643\pi$
$181$	11.0253	+	3.23733i	0.819506	+	0.240629i	0.155003	+	0.987914i	$0.450461\pi$
$182$	−1.54138	−	0.634958i	−0.114254	−	0.0470662i
$183$		−	2.02811i		−	0.149922i
$184$	−3.07461	+	1.41687i	−0.226663	+	0.104453i
$185$	14.0496	+	8.11155i	1.03295	+	0.596373i
$186$	0.449547	+	0.631300i	0.0329624	+	0.0462892i
$187$	−17.9646	+	4.35817i	−1.31370	+	0.318701i
$188$	−5.65995	+	4.90438i	−0.412794	+	0.357688i
$189$	−2.63615	+	0.225250i	−0.191751	+	0.0163845i
$190$	−1.80083	+	2.07827i	−0.130646	+	0.150774i
$191$	−8.09396	−	20.2177i	−0.585658	−	1.46290i	−0.864533	−	0.502576i	$-0.832386\pi$
$191$	−8.09396	−	20.2177i	−0.585658	−	1.46290i	0.278874	−	0.960328i	$-0.410039\pi$
$192$	7.04619	+	1.70939i	0.508515	+	0.123364i
$193$	8.94014	−	4.60896i	0.643526	−	0.331761i	−0.105385	−	0.994431i	$-0.533607\pi$
$193$	8.94014	−	4.60896i	0.643526	−	0.331761i	0.748911	+	0.662671i	$0.230577\pi$
$194$	−1.45074	+	1.14088i	−0.104157	+	0.0819101i
$195$	−2.81253	−	6.15859i	−0.201410	−	0.441026i
$196$	−6.65020	−	12.0674i	−0.475015	−	0.861957i
$197$	−0.263553	−	1.83305i	−0.0187774	−	0.130600i	0.978276	−	0.207305i	$-0.0664691\pi$
$197$	−0.263553	−	1.83305i	−0.0187774	−	0.130600i	−0.997054	+	0.0767049i	$0.975560\pi$
$198$	−0.571081	−	0.0272039i	−0.0405849	−	0.00193330i
$199$	1.67035	−	6.88526i	0.118408	−	0.488083i	−0.881467	−	0.472246i	$-0.843443\pi$
$199$	1.67035	−	6.88526i	0.118408	−	0.488083i	0.999875	−	0.0158374i	$-0.00504140\pi$
$200$	0.747172	+	0.587583i	0.0528331	+	0.0415484i
$201$	8.64214	+	1.66564i	0.609569	+	0.117485i
$202$	−1.17772	−	1.83257i	−0.0828641	−	0.128939i
$203$	16.7338	−	3.88351i	1.17448	−	0.272569i
$204$	−3.18947	+	10.8624i	−0.223308	+	0.760517i
$205$	0.385336	+	4.03542i	0.0269130	+	0.281846i
$206$	0.711218	−	1.23187i	0.0495529	−	0.0858281i
$207$	0.472223	+	4.77253i	0.0328218	+	0.331713i
$208$	11.6910	−	6.74980i	0.810624	−	0.468014i
$209$	−23.6465	−	10.7990i	−1.63566	−	0.746982i
$210$	−0.220776	+	0.872049i	−0.0152350	+	0.0601771i
$211$	6.04383	+	6.97495i	0.416074	+	0.480176i	0.924637	−	0.380849i	$-0.124368\pi$
$211$	6.04383	+	6.97495i	0.416074	+	0.480176i	−0.508563	+	0.861025i	$0.669823\pi$
$212$	−1.47384	+	2.85886i	−0.101224	+	0.196347i
$213$	−10.6108	+	3.67242i	−0.727037	+	0.251630i
$214$	−2.00927	+	2.55499i	−0.137351	+	0.174655i
$215$	−16.2051	+	16.9954i	−1.10518	+	1.15908i
$216$	−0.381638	+	0.593840i	−0.0259671	+	0.0404057i
$217$	7.46153	+	8.78639i	0.506522	+	0.596459i
$218$	−0.268255	+	0.122508i	−0.0181685	+	0.00829729i
$219$	−2.71818	+	3.81715i	−0.183678	+	0.257939i
$220$	4.49430	−	11.2262i	0.303006	−	0.756871i
$221$	9.33518	+	18.1077i	0.627952	+	1.21806i
$222$	−1.09268	−	1.04187i	−0.0733359	−	0.0699257i
$223$	12.8963	+	1.85421i	0.863599	+	0.124167i	0.559859	−	0.828588i	$-0.310855\pi$
$223$	12.8963	+	1.85421i	0.863599	+	0.124167i	0.303741	+	0.952755i	$0.401764\pi$
$224$	−5.46452	−	0.841314i	−0.365114	−	0.0562126i
$225$	1.13280	−	0.728007i	0.0755200	−	0.0485338i
$226$	2.65412	+	0.918600i	0.176549	+	0.0611044i
$227$	3.19593	−	3.04731i	0.212121	−	0.202257i	−0.576568	−	0.817049i	$-0.695608\pi$
$227$	3.19593	−	3.04731i	0.212121	−	0.202257i	0.788689	+	0.614792i	$0.210760\pi$
$228$	−12.9682	+	9.23458i	−0.858837	+	0.611575i
$229$	−3.05271	−	5.28745i	−0.201729	−	0.349405i	0.747357	−	0.664423i	$-0.231323\pi$
$229$	−3.05271	−	5.28745i	−0.201729	−	0.349405i	−0.949086	+	0.315018i	$0.897989\pi$
$230$	1.58594	+	0.378997i	0.104574	+	0.0249903i
$231$	−8.49766	+	0.320001i	−0.559105	+	0.0210545i
$232$	1.90397	−	4.16912i	0.125002	−	0.273716i
$233$	−3.55724	−	14.6631i	−0.233043	−	0.960615i	−0.961342	−	0.275356i	$-0.911204\pi$
$233$	−3.55724	−	14.6631i	−0.233043	−	0.960615i	0.728300	−	0.685259i	$-0.240311\pi$
$234$	0.119244	+	0.618694i	0.00779519	+	0.0404453i
$235$	7.26423	−	0.346038i	0.473866	−	0.0225730i
$236$	−2.72089	+	14.1173i	−0.177115	+	0.918961i
$237$	−0.685413	+	4.76715i	−0.0445224	+	0.309660i
$238$	0.538715	−	2.65266i	0.0349197	−	0.171947i
$239$	6.49594	+	4.17469i	0.420187	+	0.270038i	0.733603	−	0.679578i	$-0.237837\pi$
$239$	6.49594	+	4.17469i	0.420187	+	0.270038i	−0.313416	+	0.949616i	$0.601473\pi$
$240$	−4.50305	−	5.72610i	−0.290671	−	0.369618i
$241$	−6.02718	−	0.575526i	−0.388245	−	0.0370729i	−0.100891	−	0.994897i	$-0.532169\pi$
$241$	−6.02718	−	0.575526i	−0.388245	−	0.0370729i	−0.287354	+	0.957825i	$0.592775\pi$
$242$	0.118573	+	0.0113223i	0.00762215	+	0.000727827i
$243$	0.618159	+	0.786053i	0.0396549	+	0.0504253i
$244$	−3.35832	−	2.15826i	−0.214994	−	0.138168i
$245$	−2.16756	+	13.2030i	−0.138480	+	0.843511i
$246$	0.0536896	−	0.373419i	0.00342313	−	0.0238084i
$247$	−5.42183	+	28.1311i	−0.344983	+	1.78994i
$248$	3.07201	−	0.146338i	0.195073	−	0.00929247i
$249$	2.88304	+	14.9586i	0.182705	+	0.947966i
$250$	−0.508732	−	2.09702i	−0.0321750	−	0.132627i
$251$	7.22539	−	15.8214i	0.456062	−	0.998637i	−0.532305	−	0.846553i	$-0.678674\pi$
$251$	7.22539	−	15.8214i	0.456062	−	0.998637i	0.988367	−	0.152085i	$-0.0485987\pi$
$252$	−2.43233	+	4.60487i	−0.153222	+	0.290079i
$253$	0.786174	+	15.3942i	0.0494264	+	0.967824i
$254$	−0.419486	−	0.726571i	−0.0263209	−	0.0455891i
$255$	8.95489	−	6.37675i	0.560777	−	0.399328i
$256$	9.79087	−	9.33558i	0.611930	−	0.583474i
$257$	13.9391	+	4.82437i	0.869498	+	0.300936i	0.725150	−	0.688591i	$-0.241770\pi$
$257$	13.9391	+	4.82437i	0.869498	+	0.300936i	0.144348	+	0.989527i	$0.453892\pi$
$258$	1.83848	−	1.18152i	0.114459	−	0.0735584i
$259$	−17.5125	−	14.0565i	−1.08817	−	0.873427i
$260$	−13.1910	−	1.89657i	−0.818069	−	0.117621i
$261$	−4.69911	−	4.48059i	−0.290868	−	0.277342i
$262$	0.907910	+	1.76110i	0.0560909	+	0.108801i
$263$	−2.85349	+	7.12769i	−0.175954	+	0.439512i	−0.989961	−	0.141344i	$-0.954858\pi$
$263$	−2.85349	+	7.12769i	−0.175954	+	0.439512i	0.814007	+	0.580856i	$0.197282\pi$
$264$	−1.31605	+	1.84813i	−0.0809970	+	0.113744i
$265$	2.84108	−	1.29748i	0.174526	−	0.0797034i
$266$	2.90143	−	2.46394i	0.177898	−	0.151074i
$267$	−3.05230	+	4.74948i	−0.186798	+	0.290663i
$268$	11.9548	−	12.5379i	0.730259	−	0.765873i
$269$	−3.42776	+	4.35875i	−0.208994	+	0.265758i	−0.879237	−	0.476384i	$-0.841947\pi$
$269$	−3.42776	+	4.35875i	−0.208994	+	0.265758i	0.670243	+	0.742141i	$0.266190\pi$
$270$	0.321303	−	0.111204i	0.0195539	−	0.00676766i
$271$	−2.81244	+	5.45537i	−0.170843	+	0.331390i	−0.958676	−	0.284499i	$-0.908173\pi$
$271$	−2.81244	+	5.45537i	−0.170843	+	0.331390i	0.787833	+	0.615889i	$0.211203\pi$
$272$	14.3543	+	16.5658i	0.870359	+	1.00445i
$273$	2.55059	+	9.01783i	0.154369	+	0.545784i
$274$	2.82906	+	1.29199i	0.170910	+	0.0780518i
$275$	3.74814	−	2.16399i	0.226021	−	0.130493i
$276$	8.40530	+	4.29685i	0.505939	+	0.258640i
$277$	−8.29707	+	14.3710i	−0.498523	+	0.863467i	−0.999999	−	0.00170483i	$-0.999457\pi$
$277$	−8.29707	+	14.3710i	−0.498523	+	0.863467i	0.501476	+	0.865172i	$0.332791\pi$
$278$	0.213937	+	2.24045i	0.0128311	+	0.134373i
$279$	1.22747	−	4.18037i	0.0734865	−	0.250272i
$280$	2.43758	+	2.60798i	0.145673	+	0.155857i
$281$	13.6864	+	21.2964i	0.816462	+	1.27044i	0.959777	+	0.280762i	$0.0905873\pi$
$281$	13.6864	+	21.2964i	0.816462	+	1.27044i	−0.143315	+	0.989677i	$0.545776\pi$
$282$	−0.664572	−	0.128086i	−0.0395747	−	0.00762740i
$283$	−3.72100	−	2.92623i	−0.221191	−	0.173946i	0.501415	−	0.865207i	$-0.332813\pi$
$283$	−3.72100	−	2.92623i	−0.221191	−	0.173946i	−0.722605	+	0.691261i	$0.757056\pi$
$284$	−5.21059	+	21.4783i	−0.309191	+	1.27450i
$285$	15.4419	+	0.735589i	0.914700	+	0.0435726i
$286$	0.288207	+	2.00452i	0.0170420	+	0.118530i
$287$	0.322804	−	5.60193i	0.0190545	−	0.330672i
$288$	0.868106	+	1.90089i	0.0511536	+	0.112011i
$289$	−12.6392	+	9.93954i	−0.743480	+	0.584679i
$290$	−1.96219	+	1.01158i	−0.115224	+	0.0594018i
$291$	10.0830	+	2.44610i	0.591074	+	0.143393i
$292$	3.42816	+	8.56313i	0.200618	+	0.501119i
$293$	13.4406	−	15.5113i	0.785209	−	0.906180i	−0.212265	−	0.977212i	$-0.568084\pi$
$293$	13.4406	−	15.5113i	0.785209	−	0.906180i	0.997474	+	0.0710326i	$0.0226294\pi$
$294$	0.485718	−	1.14653i	0.0283276	−	0.0668670i
$295$	10.5511	−	9.14258i	0.614309	−	0.532301i
$296$	−5.82247	+	1.41252i	−0.338424	+	0.0821008i
$297$	1.86436	+	2.61812i	0.108181	+	0.151919i
$298$	2.39804	+	1.38451i	0.138915	+	0.0802025i
$299$	16.2829	−	4.84173i	0.941662	−	0.280004i
$300$		−	2.65052i		−	0.153028i
$301$	25.7495	−	19.8378i	1.48418	−	1.14343i
$302$	1.92775	+	0.566037i	0.110929	+	0.0325718i
$303$	−4.00535	+	11.5727i	−0.230101	+	0.664833i
$304$	1.46670	+	30.7898i	0.0841209	+	1.76591i
$305$	1.26788	+	3.66331i	0.0725988	+	0.209761i
$306$	−0.949794	+	0.380240i	−0.0542961	+	0.0217369i
$307$	−3.13845	−	10.6886i	−0.179121	−	0.610029i	−0.999282	−	0.0378961i	$-0.987934\pi$
$307$	−3.13845	−	10.6886i	−0.179121	−	0.610029i	0.820161	−	0.572133i	$-0.193884\pi$
$308$	−8.51311	+	14.4117i	−0.485080	+	0.821184i
$309$	−7.91513	+	1.13802i	−0.450276	+	0.0647399i
$310$	−1.20666	−	0.859262i	−0.0685340	−	0.0488028i
$311$	2.65334	−	27.7870i	0.150457	−	1.57566i	−0.533287	−	0.845934i	$-0.679044\pi$
$311$	2.65334	−	27.7870i	0.150457	−	1.57566i	0.683744	−	0.729722i	$-0.260350\pi$
$312$	2.32128	+	0.929299i	0.131416	+	0.0526112i
$313$	−0.457286	+	9.59962i	−0.0258473	+	0.542603i	0.948394	+	0.317094i	$0.102707\pi$
$313$	−0.457286	+	9.59962i	−0.0258473	+	0.542603i	−0.974241	+	0.225508i	$0.927596\pi$
$314$	−2.10604	+	0.618390i	−0.118851	+	0.0348978i
$315$	4.62078	−	2.05487i	0.260351	−	0.115779i
$316$	7.16448	+	6.20805i	0.403033	+	0.349230i
$317$	5.39420	+	2.78090i	0.302968	+	0.156191i	0.603007	−	0.797736i	$-0.293969\pi$
$317$	5.39420	+	2.78090i	0.302968	+	0.156191i	−0.300038	+	0.953927i	$0.597000\pi$
$318$	−0.285416	+	0.0550094i	−0.0160053	+	0.00308477i
$319$	−14.4010	−	15.1034i	−0.806303	−	0.845626i
$320$	−13.7960	+	1.31736i	−0.771218	+	0.0736424i
$321$	18.2728			1.01989
$322$	−2.08986	−	0.852542i	−0.116463	−	0.0475103i
$323$	−46.5180			−2.58833
$324$	1.95945	−	0.187104i	0.108858	−	0.0103947i
$325$	−3.29147	−	3.45200i	−0.182578	−	0.191482i
$326$	3.64810	−	0.703113i	0.202049	−	0.0389418i
$327$	1.47357	+	0.759681i	0.0814889	+	0.0420104i
$328$	−1.13143	−	0.980392i	−0.0624729	−	0.0541331i
$329$	−10.0109	−	1.05664i	−0.551920	−	0.0582547i
$330$	1.04853	−	0.307877i	0.0577199	−	0.0169481i
$331$	0.0661491	−	1.38864i	0.00363588	−	0.0763265i	−0.996320	−	0.0857104i	$-0.972684\pi$
$331$	0.0661491	−	1.38864i	0.00363588	−	0.0763265i	0.999956	+	0.00938391i	$0.00298704\pi$
$332$	27.8379	+	11.1446i	1.52780	+	0.611640i
$333$	−0.806794	+	8.44913i	−0.0442120	+	0.463009i
$334$	0.356159	+	0.253620i	0.0194882	+	0.0138775i
$335$	−16.6513	+	2.39410i	−0.909759	+	0.130804i
$336$	4.95445	+	8.78222i	0.270288	+	0.479110i
$337$	−7.24558	−	24.6762i	−0.394692	−	1.34420i	−0.882116	−	0.471032i	$-0.843882\pi$
$337$	−7.24558	−	24.6762i	−0.394692	−	1.34420i	0.487424	−	0.873165i	$-0.337936\pi$
$338$	−0.0748587	+	0.0299689i	−0.00407178	+	0.00163009i
$339$	−5.16411	−	14.9207i	−0.280476	−	0.810381i
$340$	−1.02961	−	21.6143i	−0.0558387	−	1.17220i
$341$	4.58004	−	13.2332i	0.248023	−	0.716615i
$342$	−1.38043	−	0.405332i	−0.0746454	−	0.0219179i
$343$	5.74633	−	17.6062i	0.310272	−	0.950648i
$344$		−	8.67249i		−	0.467589i
$345$	−3.83654	−	8.32526i	−0.206552	−	0.448217i
$346$	−2.01981	−	1.16614i	−0.108586	−	0.0626921i
$347$	−13.1925	−	18.5263i	−0.708213	−	0.994546i	−0.999284	−	0.0378444i	$-0.987951\pi$
$347$	−13.1925	−	18.5263i	−0.708213	−	0.994546i	0.291071	−	0.956702i	$-0.405989\pi$
$348$	−12.4200	+	3.01307i	−0.665783	+	0.161517i
$349$	−5.85783	+	5.07584i	−0.313562	+	0.271703i	−0.797396	−	0.603457i	$-0.793790\pi$
$349$	−5.85783	+	5.07584i	−0.313562	+	0.271703i	0.483833	+	0.875160i	$0.339244\pi$
$350$	0.0539539	+	0.631433i	0.00288396	+	0.0337515i
$351$	2.31960	−	2.67696i	0.123811	−	0.142886i
$352$	2.49630	+	6.23546i	0.133053	+	0.332351i
$353$	−22.8810	−	5.55087i	−1.21783	−	0.295443i	−0.425175	−	0.905111i	$-0.639788\pi$
$353$	−22.8810	−	5.55087i	−1.21783	−	0.295443i	−0.792657	+	0.609668i	$0.791303\pi$
$354$	−1.15484	+	0.595361i	−0.0613790	+	0.0316431i
$355$	16.8701	−	13.2668i	0.895371	−	0.704127i
$356$	4.61642	+	10.1085i	0.244670	+	0.535752i
$357$	−13.5941	+	6.83774i	−0.719477	+	0.361892i
$358$	0.173795	+	1.20877i	0.00918536	+	0.0638856i
$359$	15.4555	+	0.736235i	0.815708	+	0.0388570i	0.451289	−	0.892378i	$-0.350964\pi$
$359$	15.4555	+	0.736235i	0.815708	+	0.0388570i	0.364419	+	0.931235i	$0.381267\pi$
$360$	0.318098	−	1.31122i	0.0167652	−	0.0691073i
$361$	−36.4856	−	28.6926i	−1.92029	−	1.51014i
$362$	2.00706	+	0.386830i	0.105489	+	0.0203313i
$363$	−0.362021	−	0.563315i	−0.0190012	−	0.0295664i
$364$	17.6468	+	5.37305i	0.924944	+	0.281625i
$365$	2.52346	−	8.59411i	0.132084	−	0.449836i
$366$	−0.0342927	−	0.359130i	−0.00179251	−	0.0187720i
$367$	−14.0588	+	24.3505i	−0.733861	+	1.27109i	0.221360	+	0.975192i	$0.428951\pi$
$367$	−14.0588	+	24.3505i	−0.733861	+	1.27109i	−0.955221	+	0.295893i	$0.904383\pi$
$368$	15.7975	−	9.19298i	0.823501	−	0.479217i
$369$	−1.83670	+	1.06042i	−0.0956150	+	0.0552034i
$370$	2.62501	+	1.19880i	0.136468	+	0.0623227i
$371$	−4.16011	+	1.17664i	−0.215982	+	0.0610881i
$372$	−5.61598	−	6.48119i	−0.291175	−	0.336034i
$373$	3.75568	−	7.28500i	0.194462	−	0.377203i	−0.771364	−	0.636394i	$-0.780425\pi$
$373$	3.75568	−	7.28500i	0.194462	−	0.377203i	0.965826	+	0.259190i	$0.0834557\pi$
$374$	−3.10742	+	1.07549i	−0.160681	+	0.0556122i
$375$	−7.49876	+	9.53545i	−0.387234	+	0.492409i
$376$	−1.85341	+	1.94380i	−0.0955824	+	0.100244i
$377$	−12.4340	+	19.3476i	−0.640382	+	0.996454i
$378$	−0.462990	+	0.0844603i	−0.0238136	+	0.00434417i
$379$	16.7946	−	7.66983i	0.862679	−	0.393973i	0.0655993	−	0.997846i	$-0.479104\pi$
$379$	16.7946	−	7.66983i	0.862679	−	0.393973i	0.797080	+	0.603874i	$0.206377\pi$
$380$	17.6510	−	24.7873i	0.905475	−	1.27156i
$381$	−1.75293	+	4.37861i	−0.0898054	+	0.224323i
$382$	−1.77510	−	3.44322i	−0.0908223	−	0.176171i
$383$	11.5879	+	11.0490i	0.592112	+	0.564577i	0.925756	−	0.378122i	$-0.123430\pi$
$383$	11.5879	+	11.0490i	0.592112	+	0.564577i	−0.333644	+	0.942699i	$0.608278\pi$
$384$	5.41354	+	0.778349i	0.276258	+	0.0397200i
$385$	15.1490	−	5.89038i	0.772066	−	0.300202i
$386$	1.50516	−	0.967305i	0.0766104	−	0.0492345i
$387$	−11.6100	−	4.01828i	−0.590172	−	0.204260i
$388$	14.7805	−	14.0932i	0.750367	−	0.715474i
$389$	−0.594160	+	0.423099i	−0.0301251	+	0.0214520i	−0.595020	−	0.803711i	$-0.702856\pi$
$389$	−0.594160	+	0.423099i	−0.0301251	+	0.0214520i	0.564895	+	0.825163i	$0.308917\pi$
$390$	−0.602167	−	1.04298i	−0.0304919	−	0.0528135i
$391$	12.7232	+	24.4733i	0.643439	+	1.23767i
$392$	−2.78549	−	4.08135i	−0.140688	−	0.206139i
$393$	4.62715	−	10.1320i	0.233409	−	0.511094i
$394$	−0.0776637	−	0.320134i	−0.00391264	−	0.0161281i
$395$	−1.74218	−	9.03927i	−0.0876584	−	0.454815i
$396$	6.31932	−	0.301026i	0.317558	−	0.0151271i
$397$	−5.41758	+	28.1091i	−0.271900	+	1.41075i	0.547151	+	0.837034i	$0.315712\pi$
$397$	−5.41758	+	28.1091i	−0.271900	+	1.41075i	−0.819052	+	0.573720i	$0.805500\pi$
$398$	0.179358	−	1.24746i	0.00899039	−	0.0625295i
$399$	−20.9708	−	4.25885i	−1.04985	−	0.213209i
$400$	−4.31727	−	2.77454i	−0.215864	−	0.138727i
$401$	4.85811	+	6.17759i	0.242603	+	0.308494i	0.892072	−	0.451894i	$-0.149251\pi$
$401$	4.85811	+	6.17759i	0.242603	+	0.308494i	−0.649469	+	0.760388i	$0.725009\pi$
$402$	1.55848	+	0.148817i	0.0777300	+	0.00742231i
$403$	−15.3627	−	1.46696i	−0.765269	−	0.0730743i
$404$	14.9007	+	18.9478i	0.741337	+	0.942686i
$405$	−1.60797	−	1.03338i	−0.0799006	−	0.0513490i
$406$	2.89749	−	0.970625i	0.143800	−	0.0481713i
$407$	−3.88232	+	27.0021i	−0.192439	+	1.33845i
$408$	−0.768350	+	3.98658i	−0.0380390	+	0.197365i
$409$	1.13250	−	0.0539476i	0.0559985	−	0.00266754i	−0.0195640	−	0.999809i	$-0.506228\pi$
$409$	1.13250	−	0.0539476i	0.0559985	−	0.00266754i	0.0755625	+	0.997141i	$0.475925\pi$
$410$	0.136468	+	0.708061i	0.00673966	+	0.0349687i
$411$	−4.12205	−	16.9913i	−0.203326	−	0.838120i
$412$	−6.53864	+	14.3176i	−0.322136	+	0.705379i
$413$	−16.3604	+	10.2854i	−0.805044	+	0.506112i
$414$	0.164317	+	0.837117i	0.00807574	+	0.0411420i
$415$	−14.5591	−	25.2170i	−0.714676	−	1.23786i
$416$	6.02957	−	4.29364i	0.295624	−	0.210513i
$417$	9.15703	−	8.73121i	0.448422	−	0.427569i
$418$	−4.36983	−	1.51241i	−0.213735	−	0.0739745i
$419$	−9.37506	+	6.02499i	−0.458002	+	0.294340i	−0.749225	−	0.662315i	$-0.769574\pi$
$419$	−9.37506	+	6.02499i	−0.458002	+	0.294340i	0.291224	+	0.956655i	$0.405938\pi$
$420$	1.51469	−	9.83823i	0.0739091	−	0.480056i
$421$	−16.7211	−	2.40413i	−0.814935	−	0.117170i	−0.277771	−	0.960647i	$-0.589596\pi$
$421$	−16.7211	−	2.40413i	−0.814935	−	0.117170i	−0.537165	+	0.843477i	$0.680505\pi$
$422$	1.18816	+	1.13291i	0.0578386	+	0.0551490i
$423$	1.74346	+	3.38183i	0.0847697	+	0.164430i
$424$	−0.428704	+	1.07085i	−0.0208197	+	0.0520051i
$425$	4.49237	−	6.30864i	0.217912	−	0.306014i
$426$	−1.81682	+	0.829713i	−0.0880251	+	0.0401997i
$427$	−0.962968	−	5.27875i	−0.0466013	−	0.255457i
$428$	19.4455	−	30.2578i	0.939933	−	1.46256i
$429$	7.85637	−	8.23952i	0.379309	−	0.397808i
$430$	−2.58217	+	3.28349i	−0.124523	+	0.158344i
$431$	−2.19360	+	0.759213i	−0.105662	+	0.0365700i	−0.379387	−	0.925238i	$-0.623865\pi$
$431$	−2.19360	+	0.759213i	−0.105662	+	0.0365700i	0.273725	+	0.961808i	$0.411744\pi$
$432$	1.74637	−	3.38748i	0.0840223	−	0.162980i
$433$	−18.5481	−	21.4056i	−0.891363	−	1.02869i	−0.999403	−	0.0345415i	$-0.989003\pi$
$433$	−18.5481	−	21.4056i	−0.891363	−	1.02869i	0.108040	−	0.994147i	$-0.465543\pi$
$434$	1.46983	+	1.42970i	0.0705540	+	0.0686276i
$435$	11.2889	+	5.15548i	0.541263	+	0.247187i
$436$	2.82609	−	1.63164i	0.135345	−	0.0781415i
$437$	−7.21033	+	38.1128i	−0.344917	+	1.82318i
$438$	−0.416783	+	0.721889i	−0.0199146	+	0.0344932i
$439$	−2.14898	−	22.5051i	−0.102565	−	1.07411i	−0.889457	−	0.457020i	$-0.848917\pi$
$439$	−2.14898	−	22.5051i	−0.102565	−	1.07411i	0.786891	−	0.617092i	$-0.211689\pi$
$440$	1.22177	−	4.16096i	0.0582455	−	0.198366i
$441$	−6.75440	+	1.83795i	−0.321638	+	0.0875215i
$442$	1.95922	+	3.04860i	0.0931905	+	0.145007i
$443$	13.5149	+	2.60478i	0.642112	+	0.123757i	0.499905	−	0.866080i	$-0.333368\pi$
$443$	13.5149	+	2.60478i	0.642112	+	0.123757i	0.142206	+	0.989837i	$0.454580\pi$
$444$	13.1322	+	10.3273i	0.623229	+	0.490112i
$445$	2.54412	−	10.4870i	0.120603	−	0.497132i
$446$	2.31498	+	0.110276i	0.109617	+	0.00522172i
$447$	−2.21536	−	15.4082i	−0.104783	−	0.728782i
$448$	19.1514	+	1.10358i	0.904821	+	0.0521391i
$449$	−2.80702	−	6.14653i	−0.132472	−	0.290072i	0.831759	−	0.555137i	$-0.187334\pi$
$449$	−2.80702	−	6.14653i	−0.132472	−	0.290072i	−0.964231	+	0.265064i	$0.914607\pi$
$450$	0.188282	−	0.148067i	0.00887572	−	0.00697994i
$451$	−6.05882	+	3.12354i	−0.285299	+	0.147082i
$452$	−30.2025	−	7.32705i	−1.42061	−	0.344636i
$453$	−4.19783	−	10.4857i	−0.197231	−	0.492660i
$454$	0.514397	−	0.593646i	0.0241419	−	0.0278612i
$455$	−10.2446	−	14.6941i	−0.480275	−	0.688872i
$456$	−4.31482	+	3.73881i	−0.202060	+	0.175086i
$457$	22.2190	−	5.39028i	1.03936	−	0.252147i	0.320464	−	0.947261i	$-0.396161\pi$
$457$	22.2190	−	5.39028i	1.03936	−	0.252147i	0.718899	+	0.695114i	$0.244646\pi$
$458$	−0.629967	−	0.884665i	−0.0294364	−	0.0413377i
$459$	4.98091	+	2.87573i	0.232489	+	0.134228i
$460$	−17.8685	−	2.50666i	−0.833121	−	0.116873i
$461$		−	28.2854i		−	1.31738i	−0.752412	−	0.658692i	$-0.771110\pi$
$461$		−	28.2854i		−	1.31738i	0.752412	−	0.658692i	$-0.228890\pi$
$462$	−1.49932	+	0.200349i	−0.0697549	+	0.00932110i
$463$	−1.42669	−	0.418913i	−0.0663037	−	0.0194685i	0.248412	−	0.968654i	$-0.420091\pi$
$463$	−1.42669	−	0.418913i	−0.0663037	−	0.0194685i	−0.314716	+	0.949186i	$0.601909\pi$
$464$	−8.09339	+	23.3843i	−0.375726	+	1.08559i
$465$	0.396247	+	8.31824i	0.0183755	+	0.385749i
$466$	−0.877838	−	2.53635i	−0.0406651	−	0.117494i
$467$	3.39911	−	1.36080i	0.157292	−	0.0629702i	−0.291681	−	0.956516i	$-0.594214\pi$
$467$	3.39911	−	1.36080i	0.157292	−	0.0629702i	0.448972	+	0.893546i	$0.351790\pi$
$468$	−1.96429	−	6.68976i	−0.0907994	−	0.309234i
$469$	23.2846	+	0.231925i	1.07518	+	0.0107093i
$470$	1.28047	−	0.184104i	0.0590637	−	0.00849208i
$471$	10.0514	+	7.15755i	0.463143	+	0.329803i
$472$	−0.490107	+	5.13263i	−0.0225590	+	0.236249i
$473$	−36.6590	−	14.6760i	−1.68558	−	0.674805i
$474$	−0.0407639	+	0.855740i	−0.00187235	+	0.0393054i
$475$	10.4499	−	3.06836i	0.479473	−	0.140786i
$476$	−3.14398	+	29.7869i	−0.144104	+	1.36528i
$477$	1.23494	+	1.07008i	0.0565439	+	0.0489955i
$478$	1.22087	+	0.629400i	0.0558411	+	0.0287881i
$479$	8.88139	−	1.71175i	0.405801	−	0.0782118i	0.0177338	−	0.999843i	$-0.494355\pi$
$479$	8.88139	−	1.71175i	0.405801	−	0.0782118i	0.388067	+	0.921631i	$0.373143\pi$
$480$	−2.75639	−	2.89081i	−0.125811	−	0.131947i
$481$	29.9279	−	2.85777i	1.36460	−	0.130303i
$482$	−1.07700			−0.0490561
$483$	3.49515	+	12.1977i	0.159035	+	0.555015i
$484$	−1.31804			−0.0599109
$485$	−19.7418	+	1.88511i	−0.896428	+	0.0855985i
$486$	0.122752	+	0.128739i	0.00556816	+	0.00583972i
$487$	3.73861	−	0.720558i	0.169412	−	0.0326516i	−0.103840	−	0.994594i	$-0.533113\pi$
$487$	3.73861	−	0.720558i	0.169412	−	0.0326516i	0.273252	+	0.961942i	$0.411901\pi$
$488$	−1.27249	−	0.656014i	−0.0576029	−	0.0296964i
$489$	−15.7846	−	13.6774i	−0.713803	−	0.618514i
$490$	−0.160577	+	2.37460i	−0.00725413	+	0.107273i
$491$	14.1579	−	4.15714i	0.638937	−	0.187609i	0.0538111	−	0.998551i	$-0.482863\pi$
$491$	14.1579	−	4.15714i	0.638937	−	0.187609i	0.585126	+	0.810942i	$0.301045\pi$
$492$	−0.198635	+	4.16985i	−0.00895514	+	0.187991i
$493$	−34.6685	−	13.8792i	−1.56139	−	0.625086i
$494$	−0.484416	+	5.07303i	−0.0217949	+	0.228247i
$495$	−5.00427	−	3.56352i	−0.224925	−	0.160169i
$496$	−16.4356	+	2.36308i	−0.737980	+	0.106106i
$497$	−25.8740	+	14.5967i	−1.16061	+	0.654751i
$498$	0.763450	+	2.60007i	0.0342110	+	0.116512i
$499$	−6.91242	+	2.76732i	−0.309442	+	0.123882i	−0.521186	−	0.853443i	$-0.674510\pi$
$499$	−6.91242	+	2.76732i	−0.309442	+	0.123882i	0.211743	+	0.977325i	$0.432086\pi$
$500$	7.80965	+	22.5645i	0.349258	+	1.00912i
$501$	−0.116956	−	2.45521i	−0.00522521	−	0.109691i
$502$	1.01193	−	2.92377i	0.0451644	−	0.130494i
$503$	28.8822	+	8.48058i	1.28779	+	0.378130i	0.852769	−	0.522288i	$-0.174921\pi$
$503$	28.8822	+	8.48058i	1.28779	+	0.378130i	0.435025	+	0.900419i	$0.356740\pi$
$504$	−0.711363	+	1.72685i	−0.0316866	+	0.0769200i
$505$		−	23.4074i		−	1.04161i
$506$	0.399509	+	2.71265i	0.0177603	+	0.120592i
$507$	0.392574	+	0.226653i	0.0174348	+	0.0100660i
$508$	5.38507	+	7.56227i	0.238924	+	0.335521i
$509$	10.3568	−	2.51252i	0.459055	−	0.111366i	0.000438788	−	1.00000i	$-0.499860\pi$
$509$	10.3568	−	2.51252i	0.459055	−	0.111366i	0.458616	+	0.888634i	$0.348345\pi$
$510$	1.47788	−	1.28059i	0.0654415	−	0.0567053i
$511$	−5.26245	+	11.2259i	−0.232797	+	0.496605i
$512$	8.73902	−	10.0854i	0.386214	−	0.445714i
$513$	3.00602	+	7.50867i	0.132719	+	0.331516i
$514$	2.54986	+	0.618590i	0.112470	+	0.0272848i
$515$	13.5854	−	7.00378i	0.598646	−	0.308623i
$516$	−19.0089	+	14.9488i	−0.836821	+	0.658084i
$517$	5.08009	+	11.1238i	0.223422	+	0.489226i
$518$	−3.33872	−	2.19296i	−0.146695	−	0.0963530i
$519$	1.86595	+	12.9780i	0.0819060	+	0.569669i
$520$	−4.77381	−	0.227405i	−0.209346	−	0.00997236i
$521$	7.53057	−	31.0414i	0.329920	−	1.35995i	−0.529339	−	0.848410i	$-0.677560\pi$
$521$	7.53057	−	31.0414i	0.329920	−	1.35995i	0.859260	−	0.511540i	$-0.170925\pi$
$522$	−0.907862	−	0.713950i	−0.0397360	−	0.0312488i
$523$	−15.6371	−	3.01381i	−0.683765	−	0.131785i	−0.164473	−	0.986382i	$-0.552592\pi$
$523$	−15.6371	−	3.01381i	−0.683765	−	0.131785i	−0.519292	+	0.854597i	$0.673804\pi$
$524$	−11.8534	−	18.4443i	−0.517820	−	0.805743i
$525$	2.60278	−	2.43272i	0.113595	−	0.106173i
$526$	−0.384766	+	1.31039i	−0.0167766	+	0.0571359i
$527$	−2.38194	−	24.9448i	−0.103759	−	1.08661i
$528$	6.12469	−	10.6083i	0.266543	−	0.461666i
$529$	22.0234	−	6.63088i	0.957540	−	0.288299i
$530$	0.481149	−	0.277792i	0.0208998	−	0.0120665i
$531$	6.64408	+	3.03425i	0.288328	+	0.131675i
$532$	−29.3688	+	30.1932i	−1.27330	+	1.30904i
$533$	4.91952	+	5.67742i	0.213088	+	0.245917i
$534$	−0.460183	+	0.892630i	−0.0199141	+	0.0386279i
$535$	−33.0057	+	11.4234i	−1.42696	+	0.493876i
$536$	3.84046	−	4.88355i	0.165883	−	0.210937i
$537$	4.73756	−	4.96861i	0.204441	−	0.214411i
$538$	−0.533274	+	0.829790i	−0.0229911	+	0.0357748i
$539$	−21.9658	+	4.86769i	−0.946132	+	0.209666i
$540$	−3.42232	+	1.56292i	−0.147273	+	0.0672574i
$541$	−1.63512	+	2.29620i	−0.0702992	+	0.0987215i	−0.848229	−	0.529630i	$-0.822331\pi$
$541$	−1.63512	+	2.29620i	−0.0702992	+	0.0987215i	0.777929	+	0.628352i	$0.216270\pi$
$542$	−0.405773	+	1.01357i	−0.0174294	+	0.0435366i
$543$	−5.26538	−	10.2134i	−0.225959	−	0.438300i
$544$	8.69856	+	8.29406i	0.372948	+	0.355605i
$545$	−3.13660	−	0.450974i	−0.134357	−	0.0193176i
$546$	0.604130	+	1.55372i	0.0258544	+	0.0664930i
$547$	34.1929	−	21.9745i	1.46198	−	0.939560i	0.463412	−	0.886143i	$-0.346625\pi$
$547$	34.1929	−	21.9745i	1.46198	−	0.939560i	0.998572	−	0.0534174i	$-0.0170114\pi$
$548$	−32.5223	−	11.2561i	−1.38928	−	0.480836i
$549$	−1.46781	+	1.39955i	−0.0626446	+	0.0597315i
$550$	0.627116	−	0.446567i	0.0267403	−	0.0190417i
$551$	−26.2572	−	45.4789i	−1.11860	−	1.93747i
$552$	3.14716	+	1.24744i	0.133952	+	0.0530947i
$553$	0.479508	+	12.7334i	0.0203908	+	0.541478i
$554$	−1.22622	+	2.68505i	−0.0520971	+	0.114077i
$555$	−3.82474	−	15.7658i	−0.162351	−	0.669221i
$556$	−4.71323	−	24.4545i	−0.199885	−	1.03710i
$557$	−12.3081	+	0.586309i	−0.521513	+	0.0248427i	−0.306688	−	0.951810i	$-0.599221\pi$
$557$	−12.3081	+	0.586309i	−0.521513	+	0.0248427i	−0.214824	+	0.976653i	$0.568918\pi$
$558$	0.146671	−	0.760999i	0.00620906	−	0.0322157i
$559$	−6.19322	+	43.0748i	−0.261945	+	1.82187i
$560$	−14.4394	−	12.7658i	−0.610174	−	0.539452i
$561$	15.5512	+	9.99413i	0.656571	+	0.421953i
$562$	2.78363	+	3.53968i	0.117420	+	0.149312i
$563$	42.3363	+	4.04263i	1.78426	+	0.170377i	0.934305	−	0.356474i	$-0.116021\pi$
$563$	42.3363	+	4.04263i	1.78426	+	0.170377i	0.849958	+	0.526850i	$0.176627\pi$
$564$	7.45528	+	0.711893i	0.313924	+	0.0299761i
$565$	18.6556	+	23.7225i	0.784845	+	0.998012i
$566$	−0.708381	−	0.455249i	−0.0297755	−	0.0191355i
$567$	1.98217	+	1.75243i	0.0832433	+	0.0735951i
$568$	−1.12799	+	7.84537i	−0.0473296	+	0.329184i
$569$	2.29782	−	11.9222i	0.0963296	−	0.499806i	−0.901431	−	0.432922i	$-0.857482\pi$
$569$	2.29782	−	11.9222i	0.0963296	−	0.499806i	0.997761	−	0.0668831i	$-0.0213055\pi$
$570$	2.74684	−	0.130848i	0.115052	−	0.00548062i
$571$	−1.47997	−	7.67881i	−0.0619348	−	0.321348i	0.937726	−	0.347375i	$-0.112927\pi$
$571$	−1.47997	−	7.67881i	−0.0619348	−	0.321348i	−0.999661	+	0.0260263i	$0.991715\pi$
$572$	−5.28318	−	21.7776i	−0.220901	−	0.910565i
$573$	−9.04679	+	19.8097i	−0.377935	+	0.827563i
$574$	−0.0375607	−	0.997428i	−0.00156775	−	0.0416318i
$575$	−4.47244	−	4.65850i	−0.186513	−	0.194273i
$576$	−3.62529	−	6.27918i	−0.151054	−	0.261633i
$577$	−0.948923	+	0.675725i	−0.0395042	+	0.0281308i	−0.599638	−	0.800271i	$-0.704689\pi$
$577$	−0.948923	+	0.675725i	−0.0395042	+	0.0281308i	0.560134	+	0.828402i	$0.310750\pi$
$578$	−2.07003	+	1.97377i	−0.0861019	+	0.0820980i
$579$	−9.50507	−	3.28974i	−0.395017	−	0.136717i
$580$	20.5503	−	13.2069i	0.853305	−	0.548386i
$581$	14.6065	+	37.5654i	0.605980	+	1.55848i
$582$	1.82682	+	0.262656i	0.0757240	+	0.0108875i
$583$	3.80105	+	3.62430i	0.157424	+	0.150103i
$584$	1.51576	+	2.94017i	0.0627226	+	0.121665i
$585$	−2.51631	+	6.28544i	−0.104037	+	0.259871i
$586$	2.11774	−	2.97395i	0.0874829	−	0.122853i
$587$	30.6315	−	13.9889i	1.26430	−	0.577385i	0.333440	−	0.942771i	$-0.391790\pi$
$587$	30.6315	−	13.9889i	1.26430	−	0.577385i	0.930856	+	0.365387i	$0.119063\pi$
$588$	−4.14442	+	13.1404i	−0.170913	+	0.541902i
$589$	19.0513	−	29.6444i	0.784995	−	1.22148i
$590$	1.71376	−	1.79734i	0.0705544	−	0.0739953i
$591$	−1.14477	+	1.45570i	−0.0470896	+	0.0598793i
$592$	30.5683	−	10.5798i	1.25635	−	0.434826i
$593$	−10.1227	+	19.6353i	−0.415688	+	0.806323i	−0.999986	−	0.00521607i	$-0.998340\pi$
$593$	−10.1227	+	19.6353i	−0.415688	+	0.806323i	0.584298	+	0.811539i	$0.301370\pi$
$594$	0.374402	+	0.432083i	0.0153619	+	0.0177286i
$595$	20.2800	−	20.8493i	0.831399	−	0.854737i
$596$	−27.8718	−	12.7286i	−1.14167	−	0.521384i
$597$	−6.13577	+	3.54249i	−0.251120	+	0.144984i
$598$	2.80144	−	1.13268i	0.114559	−	0.0463186i
$599$	−4.01942	+	6.96183i	−0.164229	+	0.284453i	−0.936381	−	0.350985i	$-0.885847\pi$
$599$	−4.01942	+	6.96183i	−0.164229	+	0.284453i	0.772152	+	0.635438i	$0.219180\pi$
$600$	−0.0903542	−	0.946232i	−0.00368870	−	0.0386298i
$601$	−0.246162	+	0.838349i	−0.0100411	+	0.0341970i	−0.964361	−	0.264589i	$-0.914764\pi$
$601$	−0.246162	+	0.838349i	−0.0100411	+	0.0341970i	0.954320	+	0.298786i	$0.0965818\pi$
$602$	4.22420	−	3.94820i	0.172166	−	0.160916i
$603$	−4.75828	−	7.40403i	−0.193772	−	0.301515i
$604$	−21.8303	−	4.20745i	−0.888264	−	0.171199i
$605$	1.00607	+	0.791181i	0.0409025	+	0.0321661i
$606$	−0.513572	+	2.11697i	−0.0208624	+	0.0859962i
$607$	−28.5159	−	1.35838i	−1.15743	−	0.0551350i	−0.539931	−	0.841710i	$-0.681550\pi$
$607$	−28.5159	−	1.35838i	−1.15743	−	0.0551350i	−0.617495	+	0.786575i	$0.711853\pi$
$608$	2.40538	+	16.7298i	0.0975509	+	0.678482i
$609$	−14.3583	−	9.43088i	−0.581826	−	0.382158i
$610$	0.286454	+	0.627247i	0.0115982	+	0.0253965i
$611$	10.5937	−	8.33097i	0.428575	−	0.337035i
$612$	10.0624	−	5.18755i	0.406750	−	0.209694i
$613$	−9.76494	−	2.36895i	−0.394402	−	0.0956809i	0.0336529	−	0.999434i	$-0.489286\pi$
$613$	−9.76494	−	2.36895i	−0.394402	−	0.0956809i	−0.428055	+	0.903753i	$0.640801\pi$
$614$	−0.736475	−	1.83962i	−0.0297217	−	0.0742412i
$615$	2.65466	−	3.06364i	0.107046	−	0.123538i
$616$	−2.54789	+	5.43518i	−0.102657	+	0.218990i
$617$	29.4942	−	25.5569i	1.18739	−	1.02888i	0.188489	−	0.982075i	$-0.439641\pi$
$617$	29.4942	−	25.5569i	1.18739	−	1.02888i	0.998904	−	0.0468062i	$-0.0149043\pi$
$618$	−1.38234	+	0.335352i	−0.0556058	+	0.0134898i
$619$	−24.0959	−	33.8380i	−0.968497	−	1.36006i	−0.932680	−	0.360705i	$-0.882536\pi$
$619$	−24.0959	−	33.8380i	−0.968497	−	1.36006i	−0.0358171	−	0.999358i	$-0.511403\pi$
$620$	14.1958	+	8.19592i	0.570115	+	0.329156i
$621$	3.12817	−	3.63518i	0.125529	−	0.145875i
$622$		−	4.96528i		−	0.199090i
$623$	−5.68942	+	13.8112i	−0.227942	+	0.553334i
$624$	−12.9528	−	3.80327i	−0.518526	−	0.152253i
$625$	5.38156	−	15.5490i	0.215262	−	0.621960i
$626$	0.0813429	+	1.70760i	0.00325112	+	0.0682493i
$627$	8.50235	+	24.5659i	0.339551	+	0.981069i
$628$	22.5485	−	9.02707i	0.899784	−	0.360219i
$629$	13.7530	+	46.8385i	0.548368	+	1.86757i
$630$	0.783485	−	0.442000i	0.0312148	−	0.0176097i
$631$	−33.7681	+	4.85512i	−1.34429	+	0.193279i	−0.776615	−	0.629976i	$-0.783065\pi$
$631$	−33.7681	+	4.85512i	−1.34429	+	0.193279i	−0.567671	+	0.823255i	$0.692156\pi$
$632$	2.76934	+	1.97204i	0.110158	+	0.0784435i
$633$	0.877290	−	9.18739i	0.0348691	−	0.365166i
$634$	1.00221	+	0.401223i	0.0398027	+	0.0159346i
$635$	0.428952	−	9.00482i	0.0170225	−	0.357345i
$636$	3.08612	−	0.906166i	0.122373	−	0.0359318i
$637$	10.9205	+	22.2605i	0.432684	+	0.881995i
$638$	−2.80546	−	2.43094i	−0.111069	−	0.0962420i
$639$	9.98012	+	5.14511i	0.394807	+	0.203537i
$640$	−10.2649	+	1.97840i	−0.405756	+	0.0782031i
$641$	14.7139	+	15.4315i	0.581165	+	0.609508i	0.947024	−	0.321162i	$-0.104073\pi$
$641$	14.7139	+	15.4315i	0.581165	+	0.609508i	−0.365860	+	0.930670i	$0.619225\pi$
$642$	3.23568	−	0.308970i	0.127702	−	0.0121941i
$643$	6.33833			0.249959			0.124980	−	0.992159i	$-0.460113\pi$
$643$	6.33833			0.249959			0.124980	+	0.992159i	$0.460113\pi$
$644$	23.9175	+	7.19290i	0.942481	+	0.283440i
$645$	23.4829			0.924640
$646$	−8.23723	+	0.786560i	−0.324089	+	0.0309468i
$647$	−24.4035	−	25.5936i	−0.959400	−	1.00619i	−0.999975	−	0.00701323i	$-0.997768\pi$
$647$	−24.4035	−	25.5936i	−0.959400	−	1.00619i	0.0405755	−	0.999176i	$-0.487081\pi$
$648$	0.693142	−	0.133592i	0.0272292	−	0.00524800i
$649$	20.8664	+	10.7574i	0.819080	+	0.422265i
$650$	−0.641210	−	0.555612i	−0.0251503	−	0.0217929i
$651$	1.20996	−	11.4635i	0.0474221	−	0.449289i
$652$	−39.4458	+	11.5823i	−1.54482	+	0.453599i
$653$	−1.34094	+	28.1498i	−0.0524750	+	1.10159i	0.807047	+	0.590487i	$0.201064\pi$
$653$	−1.34094	+	28.1498i	−0.0524750	+	1.10159i	−0.859522	+	0.511098i	$0.829239\pi$
$654$	0.273780	+	0.109605i	0.0107057	+	0.00428590i
$655$	−2.02377	+	21.1939i	−0.0790753	+	0.828114i
$656$	6.58410	+	4.68852i	0.257066	+	0.183056i
$657$	4.63837	−	0.666896i	0.180960	−	0.0260181i
$658$	−1.79056	−	0.0178348i	−0.0698034	−	0.000695273i
$659$	7.25238	+	24.6993i	0.282513	+	0.962150i	0.971433	+	0.237313i	$0.0762666\pi$
$659$	7.25238	+	24.6993i	0.282513	+	0.962150i	−0.688921	+	0.724837i	$0.741915\pi$
$660$	−11.2262	+	4.49430i	−0.436980	+	0.174940i
$661$	0.978841	+	2.82818i	0.0380725	+	0.110003i	0.962435	−	0.271512i	$-0.0875236\pi$
$661$	0.978841	+	2.82818i	0.0380725	+	0.110003i	−0.924363	+	0.381515i	$0.875402\pi$
$662$	−0.0117667	−	0.247014i	−0.000457326	−	0.00960046i
$663$	6.66317	−	19.2520i	0.258776	−	0.747684i
$664$	10.3180	+	3.02964i	0.400417	+	0.117573i
$665$	40.5415	−	5.41741i	1.57213	−	0.210078i
$666$			1.50978i			0.0585029i
$667$	−16.7450	+	26.2530i	−0.648370	+	1.01652i
$668$	−4.19002	−	2.41911i	−0.162117	−	0.0935980i
$669$	−7.55751	−	10.6130i	−0.292190	−	0.410324i
$670$	−2.90807	+	0.705491i	−0.112349	+	0.0272555i
$671$	−4.92637	+	4.26872i	−0.190180	+	0.164792i
$672$	3.16207	+	4.53543i	0.121979	+	0.174958i
$673$	−5.92215	+	6.83453i	−0.228282	+	0.263452i	−0.858322	−	0.513111i	$-0.828493\pi$
$673$	−5.92215	+	6.83453i	−0.228282	+	0.263452i	0.630040	+	0.776563i	$0.283038\pi$
$674$	−1.70026	−	4.24705i	−0.0654917	−	0.163590i
$675$	−1.30861	−	0.317464i	−0.0503682	−	0.0122192i
$676$	0.793078	−	0.408860i	0.0305030	−	0.0157254i
$677$	4.14040	−	3.25605i	0.159129	−	0.125140i	−0.535420	−	0.844586i	$-0.679847\pi$
$677$	4.14040	−	3.25605i	0.159129	−	0.125140i	0.694548	+	0.719446i	$0.255604\pi$
$678$	−1.16673	−	2.55478i	−0.0448080	−	0.0981159i
$679$	27.4054	+	1.57920i	1.05172	+	0.0606040i
$680$	−1.10439	−	7.68118i	−0.0423513	−	0.294560i
$681$	−4.41089	−	0.210117i	−0.169026	−	0.00805169i
$682$	0.587260	−	2.42072i	0.0224874	−	0.0926942i
$683$	27.7603	+	21.8309i	1.06222	+	0.835337i	0.986821	−	0.161817i	$-0.0517354\pi$
$683$	27.7603	+	21.8309i	1.06222	+	0.835337i	0.0753963	+	0.997154i	$0.475978\pi$
$684$	15.6324	+	3.01291i	0.597721	+	0.115201i
$685$	18.0678	+	28.1140i	0.690334	+	1.07418i
$686$	0.719839	−	3.21481i	0.0274836	−	0.122742i
$687$	−1.72010	+	5.85811i	−0.0656258	+	0.223501i
$688$	4.45079	+	46.6108i	0.169685	+	1.77702i
$689$	2.89402	−	5.01259i	0.110253	−	0.190964i
$690$	−0.820130	−	1.40934i	−0.0312218	−	0.0536525i
$691$	−32.8985	+	18.9940i	−1.25152	+	0.722564i	−0.971411	−	0.237404i	$-0.923703\pi$
$691$	−32.8985	+	18.9940i	−1.25152	+	0.722564i	−0.280107	+	0.959969i	$0.590370\pi$
$692$	23.4757	+	10.7210i	0.892414	+	0.407552i
$693$	6.09566	+	5.92922i	0.231555	+	0.225233i
$694$	−2.64934	−	3.05751i	−0.100568	−	0.116061i
$695$	−11.0817	+	21.4955i	−0.420353	+	0.815371i
$696$	−4.33123	+	1.49905i	−0.164175	+	0.0568214i
$697$	−7.54027	+	9.58823i	−0.285608	+	0.363180i
$698$	−0.951456	+	0.997859i	−0.0360132	+	0.0377695i
$699$	−8.15744	+	12.6932i	−0.308543	+	0.480102i
$700$	−1.25850	−	6.89876i	−0.0475667	−	0.260749i
$701$	40.6045	−	18.5435i	1.53361	−	0.700377i	0.543339	−	0.839513i	$-0.317160\pi$
$701$	40.6045	−	18.5435i	1.53361	−	0.700377i	0.990273	+	0.139136i	$0.0444326\pi$
$702$	0.365483	−	0.513248i	0.0137943	−	0.0193713i
$703$	−25.5137	+	63.7303i	−0.962269	+	2.40363i
$704$	−10.6785	−	20.7134i	−0.402462	−	0.780667i
$705$	−5.26333	−	5.01857i	−0.198228	−	0.189010i
$706$	−4.14554	−	0.596038i	−0.156019	−	0.0224322i
$707$	−4.93026	+	32.0231i	−0.185421	+	1.20435i
$708$	12.0948	−	7.77288i	0.454552	−	0.292123i
$709$	−5.83056	−	2.01798i	−0.218971	−	0.0757867i	0.215380	−	0.976530i	$-0.430901\pi$
$709$	−5.83056	−	2.01798i	−0.218971	−	0.0757867i	−0.434351	+	0.900744i	$0.643022\pi$
$710$	2.76297	−	2.63448i	0.103692	−	0.0988704i
$711$	3.92314	−	2.79366i	0.147129	−	0.104770i
$712$	1.99265	+	3.45137i	0.0746777	+	0.129346i
$713$	−20.8068	−	1.91491i	−0.779221	−	0.0717140i
$714$	−2.29158	+	1.44066i	−0.0857602	+	0.0539154i
$715$	−9.03974	+	19.7943i	−0.338067	+	0.740264i
$716$	−3.18587	−	13.1323i	−0.119062	−	0.490779i
$717$	−1.46135	−	7.58220i	−0.0545751	−	0.283162i
$718$	2.74925	−	0.130963i	0.102601	−	0.00488748i
$719$	7.00297	−	36.3349i	0.261167	−	1.35506i	−0.580146	−	0.814513i	$-0.697004\pi$
$719$	7.00297	−	36.3349i	0.261167	−	1.35506i	0.841313	−	0.540549i	$-0.181783\pi$
$720$	−1.03671	+	7.21047i	−0.0386359	+	0.268718i
$721$	−20.0611	+	6.72024i	−0.747116	+	0.250275i
$722$	−6.94589	−	4.46385i	−0.258499	−	0.166127i
$723$	3.74270	+	4.75923i	0.139193	+	0.176998i
$724$	−22.5156	−	2.14998i	−0.836784	−	0.0799032i
$725$	8.70346	+	0.831080i	0.323238	+	0.0308655i
$726$	−0.0736302	−	0.0936285i	−0.00273267	−	0.00347488i
$727$	1.90950	+	1.22716i	0.0708194	+	0.0455129i	0.575571	−	0.817752i	$-0.304780\pi$
$727$	1.90950	+	1.22716i	0.0708194	+	0.0455129i	−0.504752	+	0.863264i	$0.668416\pi$
$728$	6.48306	+	1.31661i	0.240278	+	0.0487968i
$729$	0.142315	−	0.989821i	0.00527092	−	0.0366601i
$730$	0.301529	−	1.56448i	0.0111601	−	0.0579041i
$731$	−70.5809	+	3.36218i	−2.61053	+	0.124355i
$732$	0.755498	+	3.91990i	0.0279240	+	0.144884i
$733$	12.0539	+	49.6868i	0.445220	+	1.83522i	0.542621	+	0.839978i	$0.317432\pi$
$733$	12.0539	+	49.6868i	0.445220	+	1.83522i	−0.0974005	+	0.995245i	$0.531053\pi$
$734$	−2.07774	+	4.54961i	−0.0766907	+	0.167929i
$735$	11.0513	−	7.54240i	0.407632	−	0.278206i
$736$	8.14372	−	5.84126i	0.300181	−	0.215312i
$737$	−14.1439	−	24.4980i	−0.520998	−	0.902394i
$738$	−0.307306	+	0.218832i	−0.0113121	+	0.00805532i
$739$	10.5163	−	10.0272i	0.386847	−	0.368858i	−0.471554	−	0.881837i	$-0.656307\pi$
$739$	10.5163	−	10.0272i	0.386847	−	0.368858i	0.858401	+	0.512979i	$0.171458\pi$
$740$	−30.1766	−	10.4442i	−1.10931	−	0.383937i
$741$	24.1010	−	15.4887i	0.885371	−	0.568993i
$742$	−0.716761	+	0.278697i	−0.0263131	+	0.0102313i
$743$	−10.2942	−	1.48008i	−0.377657	−	0.0542989i	−0.0491274	−	0.998793i	$-0.515644\pi$
$743$	−10.2942	−	1.48008i	−0.377657	−	0.0542989i	−0.328530	+	0.944494i	$0.606553\pi$
$744$	−2.22584	−	2.12233i	−0.0816033	−	0.0778086i
$745$	13.6341	+	26.4464i	0.499514	+	0.968921i
$746$	0.541862	−	1.35351i	0.0198390	−	0.0495553i
$747$	8.83655	−	12.4092i	0.323313	−	0.454029i
$748$	33.0983	−	15.1155i	1.21019	−	0.552677i
$749$	47.5605	−	8.67615i	1.73782	−	0.317020i
$750$	−1.16662	+	1.81530i	−0.0425990	+	0.0662853i
$751$	11.0022	−	11.5388i	0.401477	−	0.421057i	−0.491698	−	0.870766i	$-0.663624\pi$
$751$	11.0022	−	11.5388i	0.401477	−	0.421057i	0.893175	+	0.449709i	$0.148472\pi$
$752$	8.96369	−	11.3983i	0.326872	−	0.415652i
$753$	−16.4366	+	5.68875i	−0.598982	+	0.207310i
$754$	−1.87462	+	3.63625i	−0.0682696	+	0.132424i
$755$	14.1376	+	16.3157i	0.514521	+	0.593789i
$756$	5.01120	−	1.41736i	0.182256	−	0.0515490i
$757$	16.3992	+	7.48927i	0.596040	+	0.272202i	0.690507	−	0.723326i	$-0.257387\pi$
$757$	16.3992	+	7.48927i	0.596040	+	0.272202i	−0.0944672	+	0.995528i	$0.530115\pi$
$758$	2.84423	−	1.64212i	0.103307	−	0.0596445i
$759$	10.5988	−	11.1922i	0.384711	−	0.406250i
$760$	5.45639	−	9.45075i	0.197924	−	0.342815i
$761$	−0.635056	−	6.65061i	−0.0230208	−	0.241084i	−0.999657	−	0.0261856i	$-0.991664\pi$
$761$	−0.635056	−	6.65061i	−0.0230208	−	0.241084i	0.976636	−	0.214899i	$-0.0689421\pi$
$762$	−0.236366	+	0.804988i	−0.00856263	+	0.0291616i
$763$	4.19612	+	1.27762i	0.151910	+	0.0462531i
$764$	23.1753	+	36.0615i	0.838453	+	1.30466i
$765$	−10.7947	−	2.08050i	−0.390282	−	0.0752206i
$766$	2.23876	+	1.76058i	0.0808896	+	0.0636123i
$767$	6.09961	−	25.1429i	0.220244	−	0.907858i
$768$	−13.5130	−	0.643701i	−0.487607	−	0.0232276i
$769$	2.63052	+	18.2957i	0.0948591	+	0.659760i	0.980664	+	0.195701i	$0.0626982\pi$
$769$	2.63052	+	18.2957i	0.0948591	+	0.659760i	−0.885804	+	0.464059i	$0.846393\pi$
$770$	2.58294	−	1.29920i	0.0930826	−	0.0468198i
$771$	−6.12753	−	13.4174i	−0.220677	−	0.483216i
$772$	−15.5625	+	12.2385i	−0.560106	+	0.440473i
$773$	−0.896996	+	0.462434i	−0.0322627	+	0.0166326i	−0.474282	−	0.880373i	$-0.657292\pi$
$773$	−0.896996	+	0.462434i	−0.0322627	+	0.0166326i	0.442020	+	0.897005i	$0.354262\pi$
$774$	−2.12381	−	0.515230i	−0.0763387	−	0.0185196i
$775$	2.18046	+	5.44653i	0.0783244	+	0.195645i
$776$	4.79620	−	5.53512i	0.172174	−	0.198699i
$777$	1.91182	+	22.3744i	0.0685862	+	0.802679i
$778$	−0.0980576	+	0.0849674i	−0.00351553	+	0.00304623i
$779$	−16.6699	+	4.04408i	−0.597262	+	0.144894i
$780$	7.73019	+	10.8555i	0.276785	+	0.388690i
$781$	31.2538	+	18.0444i	1.11835	+	0.645680i
$782$	2.66679	+	4.11851i	0.0953641	+	0.147278i
$783$			6.49287i			0.232036i
$784$	17.0653	+	20.5059i	0.609476	+	0.732354i
$785$	−22.6301	−	6.64480i	−0.807703	−	0.237163i
$786$	0.648038	−	1.87238i	0.0231148	−	0.0667857i
$787$	1.77276	+	37.2149i	0.0631921	+	1.32657i	0.778450	+	0.627706i	$0.216006\pi$
$787$	1.77276	+	37.2149i	0.0631921	+	1.32657i	−0.715258	+	0.698860i	$0.753691\pi$
$788$	1.19223	+	3.44473i	0.0424715	+	0.122713i
$789$	7.12769	−	2.85349i	0.253752	−	0.101587i
$790$	−0.461341	−	1.57118i	−0.0164138	−	0.0559001i
$791$	−20.5256	−	36.3836i	−0.729808	−	1.29365i
$792$	2.24573	−	0.322887i	0.0797985	−	0.0114733i
$793$	5.85177	+	4.16702i	0.207802	+	0.147975i
$794$	−0.484036	+	5.06905i	−0.0171778	+	0.179894i
$795$	−2.89960	−	1.16082i	−0.102838	−	0.0411702i
$796$	−0.663566	+	13.9300i	−0.0235195	+	0.493735i
$797$	−18.9377	+	5.56062i	−0.670809	+	0.196967i	−0.599363	−	0.800477i	$-0.704580\pi$
$797$	−18.9377	+	5.56062i	−0.670809	+	0.196967i	−0.0714460	+	0.997444i	$0.522761\pi$
$798$	−3.78545	−	0.399551i	−0.134003	−	0.0141440i
$799$	16.5381	+	14.3304i	0.585077	+	0.506972i
$800$	−2.50114	−	1.28943i	−0.0884287	−	0.0455882i
$801$	5.54369	−	1.06846i	0.195877	−	0.0377521i
$802$	0.964712	+	1.01176i	0.0340652	+	0.0357265i
$803$	14.9932	−	1.43168i	0.529100	−	0.0505229i
$804$	−17.3239			−0.610966
$805$	−13.9387	−	19.8473i	−0.491273	−	0.699527i
$806$	−2.74517			−0.0966944
$807$	5.52000	−	0.527096i	0.194313	−	0.0185546i
$808$	5.96545	+	6.25638i	0.209864	+	0.220099i
$809$	−26.3970	+	5.08761i	−0.928070	+	0.178871i	−0.630820	−	0.775929i	$-0.717282\pi$
$809$	−26.3970	+	5.08761i	−0.928070	+	0.178871i	−0.297250	+	0.954800i	$0.596069\pi$
$810$	−0.302206	−	0.155798i	−0.0106184	−	0.00547419i
$811$	6.24915	+	5.41492i	0.219437	+	0.190144i	0.757641	−	0.652671i	$-0.226352\pi$
$811$	6.24915	+	5.41492i	0.219437	+	0.190144i	−0.538204	+	0.842815i	$0.680897\pi$
$812$	−30.8962	+	13.7396i	−1.08424	+	0.482165i
$813$	5.88904	−	1.72918i	0.206538	−	0.0606449i
$814$	−0.230895	+	4.84708i	−0.00809286	+	0.169890i
$815$	37.0617	+	14.8373i	1.29822	+	0.519727i
$816$	2.08360	−	21.8204i	0.0729405	−	0.763867i
$817$	−80.9424	−	57.6388i	−2.83182	−	2.01653i
$818$	0.199627	−	0.0287020i	0.00697978	−	0.00100354i
$819$	4.76640	−	8.06897i	0.166552	−	0.281953i
$820$	−2.24802	−	7.65606i	−0.0785044	−	0.267361i
$821$	20.0359	−	8.02116i	0.699258	−	0.279941i	0.00533061	−	0.999986i	$-0.498303\pi$
$821$	20.0359	−	8.02116i	0.699258	−	0.279941i	0.693927	+	0.720045i	$0.255879\pi$
$822$	−1.01722	−	2.93906i	−0.0354796	−	0.102511i
$823$	0.627239	+	13.1674i	0.0218642	+	0.458986i	0.983079	+	0.183184i	$0.0586403\pi$
$823$	0.627239	+	13.1674i	0.0218642	+	0.458986i	−0.961215	+	0.275802i	$0.911057\pi$
$824$	−1.84621	+	5.33428i	−0.0643158	+	0.185828i
$825$	−4.15266	−	1.21933i	−0.144577	−	0.0424517i
$826$	−2.72313	+	2.09794i	−0.0947498	+	0.0729965i
$827$			17.9012i			0.622487i	0.950330	+	0.311244i	$0.100746\pi$
$827$			17.9012i			0.622487i	−0.950330	+	0.311244i	$0.899254\pi$
$828$	−2.69054	−	9.04837i	−0.0935028	−	0.314453i
$829$	1.90505	+	1.09988i	0.0661652	+	0.0382005i	0.532718	−	0.846293i	$-0.321171\pi$
$829$	1.90505	+	1.09988i	0.0661652	+	0.0382005i	−0.466552	+	0.884494i	$0.654504\pi$
$830$	−3.00445	−	4.21916i	−0.104286	−	0.146449i
$831$	16.1264	−	3.91222i	0.559418	−	0.135713i
$832$	−19.4095	+	16.8185i	−0.672904	+	0.583075i
$833$	−32.1361	+	24.2519i	−1.11345	+	0.840279i
$834$	1.47386	−	1.70092i	0.0510356	−	0.0588982i
$835$	1.74615	+	4.36166i	0.0604279	+	0.150941i
$836$	49.7264	+	12.0635i	1.71982	+	0.417225i
$837$	−3.87252	+	1.99643i	−0.133854	+	0.0690066i
$838$	−1.55823	+	1.22540i	−0.0538280	+	0.0423308i
$839$	−14.8986	−	32.6235i	−0.514358	−	1.12629i	−0.971532	−	0.236909i	$-0.923866\pi$
$839$	−14.8986	−	32.6235i	−0.514358	−	1.12629i	0.457174	−	0.889377i	$-0.348862\pi$
$840$	0.205363	−	3.56387i	0.00708571	−	0.122965i
$841$	−1.87248	−	13.0234i	−0.0645683	−	0.449082i
$842$	−3.00156	−	0.142982i	−0.103440	−	0.00492748i
$843$	5.96827	−	24.6015i	0.205558	−	0.847322i
$844$	−14.2797	−	11.2297i	−0.491528	−	0.386542i
$845$	−0.850788	−	0.163976i	−0.0292680	−	0.00564094i
$846$	0.365907	+	0.569363i	0.0125801	+	0.0195751i
$847$	−1.20974	−	1.29430i	−0.0415670	−	0.0444728i
$848$	1.75453	−	5.97537i	0.0602507	−	0.205195i
$849$	0.449975	+	4.71235i	0.0154431	+	0.161727i
$850$	0.688820	−	1.19307i	0.0236263	−	0.0409220i
$851$	40.5071	−	4.00802i	1.38857	−	0.137393i
$852$	19.1403	−	11.0507i	0.655736	−	0.378590i
$853$	18.5790	+	8.48475i	0.636133	+	0.290512i	0.707259	−	0.706955i	$-0.249932\pi$
$853$	18.5790	+	8.48475i	0.636133	+	0.290512i	−0.0711251	+	0.997467i	$0.522659\pi$
$854$	−0.259776	−	0.918459i	−0.00888935	−	0.0314290i
$855$	−10.1238	−	11.6835i	−0.346226	−	0.399566i
$856$	5.91055	−	11.4649i	0.202019	−	0.391861i
$857$	−23.3330	+	8.07562i	−0.797040	+	0.275858i	−0.695082	−	0.718931i	$-0.744632\pi$
$857$	−23.3330	+	8.07562i	−0.797040	+	0.275858i	−0.101958	+	0.994789i	$0.532511\pi$
$858$	1.25186	−	1.59186i	0.0427377	−	0.0543454i
$859$	−6.21239	+	6.51537i	−0.211964	+	0.222301i	−0.821130	−	0.570741i	$-0.806656\pi$
$859$	−6.21239	+	6.51537i	−0.211964	+	0.222301i	0.609166	+	0.793043i	$0.291504\pi$
$860$	24.9900	−	38.8851i	0.852150	−	1.32597i
$861$	−4.27707	+	3.63215i	−0.145762	+	0.123783i
$862$	−0.375598	+	0.171530i	−0.0127929	+	0.00584232i
$863$	−28.6300	+	40.2053i	−0.974578	+	1.36860i	−0.0454003	+	0.998969i	$0.514456\pi$
$863$	−28.6300	+	40.2053i	−0.974578	+	1.36860i	−0.929177	+	0.369634i	$0.879483\pi$
$864$	0.776675	−	1.94004i	0.0264230	−	0.0660015i
$865$	−11.4837	−	22.2752i	−0.390456	−	0.757380i
$866$	−3.64636	−	3.47680i	−0.123909	−	0.118147i
$867$	15.9156	+	2.28832i	0.540522	+	0.0777153i
$868$	−17.6946	−	14.2027i	−0.600594	−	0.482071i
$869$	13.0223	−	8.36892i	0.441751	−	0.283896i
$870$	2.08618	+	0.722032i	0.0707280	+	0.0244792i
$871$	−22.5624	+	21.5132i	−0.764497	+	0.728946i
$872$	0.953289	−	0.678834i	0.0322824	−	0.0229882i
$873$	−5.18772	−	8.98539i	−0.175578	−	0.304110i
$874$	−0.632339	+	6.87079i	−0.0213892	+	0.232408i
$875$	−14.9902	+	28.3793i	−0.506762	+	0.959397i
$876$	3.83173	−	8.39031i	0.129462	−	0.283482i
$877$	−11.2096	−	46.2065i	−0.378521	−	1.56028i	−0.768740	−	0.639562i	$-0.779116\pi$
$877$	−11.2096	−	46.2065i	−0.378521	−	1.56028i	0.390219	−	0.920722i	$-0.372399\pi$
$878$	−0.761067	−	3.94879i	−0.0256848	−	0.133265i
$879$	−20.5011	+	0.976590i	−0.691486	+	0.0329396i
$880$	−4.43102	+	22.9903i	−0.149370	+	0.775004i
$881$	−1.76274	+	12.2601i	−0.0593881	+	0.413053i	0.938342	+	0.345709i	$0.112362\pi$
$881$	−1.76274	+	12.2601i	−0.0593881	+	0.413053i	−0.997730	+	0.0673440i	$0.978548\pi$
$882$	−1.16497	+	0.439666i	−0.0392265	+	0.0148043i
$883$	10.0546	+	6.46168i	0.338363	+	0.217453i	0.698777	−	0.715340i	$-0.253728\pi$
$883$	10.0546	+	6.46168i	0.338363	+	0.217453i	−0.360414	+	0.932793i	$0.617364\pi$
$884$	−24.7883	−	31.5209i	−0.833721	−	1.06016i
$885$	−13.8979	−	1.32709i	−0.467172	−	0.0446095i
$886$	2.43721	+	0.232725i	0.0818797	+	0.00781856i
$887$	5.51916	+	7.01818i	0.185315	+	0.235648i	0.869830	−	0.493351i	$-0.164228\pi$
$887$	5.51916	+	7.01818i	0.185315	+	0.235648i	−0.684515	+	0.728999i	$0.739986\pi$
$888$	5.04025	+	3.23917i	0.169140	+	0.108699i
$889$	−2.48351	+	12.2290i	−0.0832943	+	0.410146i
$890$	0.273181	−	1.90002i	0.00915706	−	0.0636888i
$891$	0.608271	−	3.15601i	0.0203778	−	0.105730i
$892$	−25.6165	+	1.22026i	−0.857704	+	0.0408575i
$893$	5.82388	+	30.2171i	0.194889	+	1.01118i
$894$	−0.652821	−	2.69096i	−0.0218336	−	0.0899993i
$895$	−5.45116	+	11.9364i	−0.182212	+	0.398989i
$896$	14.4599	−	0.544525i	0.483072	−	0.0181913i
$897$	−14.7406	−	8.44329i	−0.492174	−	0.281913i
$898$	−0.600987	−	1.04094i	−0.0200552	−	0.0347366i
$899$	23.0431	−	16.4089i	0.768530	−	0.547268i
$900$	−1.91827	+	1.82907i	−0.0639423	+	0.0609689i
$901$	8.88131	+	3.07385i	0.295879	+	0.102405i
$902$	−1.02006	+	0.655552i	−0.0339643	+	0.0218275i
$903$	−32.1265	−	4.94617i	−1.06910	−	0.164598i
$904$	−11.0320	−	1.58617i	−0.366921	−	0.0527552i
$905$	15.8957	+	15.1565i	0.528391	+	0.503819i
$906$	−0.920637	−	1.78579i	−0.0305861	−	0.0593288i
$907$	0.491720	−	1.22826i	0.0163273	−	0.0407836i	−0.919980	−	0.391965i	$-0.871796\pi$
$907$	0.491720	−	1.22826i	0.0163273	−	0.0407836i	0.936308	+	0.351181i	$0.114220\pi$
$908$	−5.04189	+	7.08034i	−0.167321	+	0.234969i
$909$	11.1396	−	5.08726i	0.369476	−	0.168734i
$910$	−2.06254	−	2.42876i	−0.0683725	−	0.0805126i
$911$	27.3073	−	42.4909i	0.904730	−	1.40779i	−0.00833189	−	0.999965i	$-0.502652\pi$
$911$	27.3073	−	42.4909i	0.904730	−	1.40779i	0.913062	−	0.407822i	$-0.133711\pi$
$912$	21.2715	−	22.3089i	0.704369	−	0.738721i
$913$	30.2671	−	38.4877i	1.00169	−	1.27376i
$914$	3.84332	−	1.33019i	0.127126	−	0.0439987i
$915$	1.77632	−	3.44558i	0.0587234	−	0.113908i
$916$	7.86990	+	9.08234i	0.260029	+	0.300089i
$917$	7.23272	−	28.5687i	0.238845	−	0.943420i
$918$	0.930626	+	0.425003i	0.0307152	+	0.0140272i
$919$	−14.8320	+	8.56323i	−0.489261	+	0.282475i	−0.724268	−	0.689519i	$-0.757822\pi$
$919$	−14.8320	+	8.56323i	−0.489261	+	0.282475i	0.235007	+	0.971994i	$0.424489\pi$
$920$	−6.46447	−	0.285751i	−0.213127	−	0.00942093i
$921$	−5.56990	+	9.64736i	−0.183535	+	0.317891i
$922$	−0.478271	−	5.00868i	−0.0157510	−	0.164952i
$923$	11.2051	−	38.1611i	0.368821	−	1.25609i
$924$	16.3050	−	3.78400i	0.536394	−	0.124484i
$925$	−6.17900	−	9.61471i	−0.203164	−	0.316130i
$926$	−0.259716	−	0.0500561i	−0.00853478	−	0.00164494i
$927$	6.28569	+	4.94312i	0.206449	+	0.162353i
$928$	−3.19886	+	13.1859i	−0.105008	+	0.432848i
$929$	−8.25282	−	0.393130i	−0.270766	−	0.0128982i	−0.0882403	−	0.996099i	$-0.528124\pi$
$929$	−8.25282	−	0.393130i	−0.270766	−	0.0128982i	−0.182526	+	0.983201i	$0.558427\pi$
$930$	0.210817	+	1.46626i	0.00691296	+	0.0480807i
$931$	−56.6050	−	1.12773i	−1.85515	−	0.0369599i
$932$	12.3376	+	27.0156i	0.404132	+	0.884926i
$933$	−21.9414	+	17.2549i	−0.718329	+	0.564901i
$934$	0.578892	−	0.298439i	0.0189419	−	0.00976523i
$935$	−34.3375	−	8.33020i	−1.12296	−	0.272427i
$936$	−0.929299	−	2.32128i	−0.0303751	−	0.0758733i
$937$	11.0235	−	12.7218i	0.360122	−	0.415603i	−0.546559	−	0.837421i	$-0.684062\pi$
$937$	11.0235	−	12.7218i	0.360122	−	0.415603i	0.906681	+	0.421818i	$0.138608\pi$
$938$	4.12707	−	0.352645i	0.134754	−	0.0115143i
$939$	7.26313	−	6.29354i	0.237023	−	0.205382i
$940$	−13.9113	+	3.37484i	−0.453737	+	0.110075i
$941$	−27.4815	−	38.5923i	−0.895871	−	1.25807i	−0.965474	−	0.260500i	$-0.916113\pi$
$941$	−27.4815	−	38.5923i	−0.895871	−	1.25807i	0.0696032	−	0.997575i	$-0.477827\pi$
$942$	1.90089	+	1.09748i	0.0619342	+	0.0357577i
$943$	6.68702	+	7.66403i	0.217759	+	0.249575i
$944$		−	27.8372i		−	0.906022i
$945$	−4.67588	−	1.92619i	−0.152106	−	0.0626591i
$946$	−6.73958	−	1.97892i	−0.219123	−	0.0643403i
$947$	−8.25654	+	23.8557i	−0.268302	+	0.775206i	0.727702	+	0.685893i	$0.240588\pi$
$947$	−8.25654	+	23.8557i	−0.268302	+	0.775206i	−0.996004	+	0.0893130i	$0.971533\pi$
$948$	−0.451075	−	9.46922i	−0.0146502	−	0.307546i
$949$	−5.42889	−	15.6857i	−0.176229	−	0.509181i
$950$	1.79854	−	0.720028i	0.0583524	−	0.0233608i
$951$	−1.70979	−	5.82301i	−0.0554437	−	0.188824i
$952$	−0.106986	+	10.7411i	−0.00346743	+	0.348120i
$953$	4.65385	−	0.669123i	0.150753	−	0.0216750i	−0.0665250	−	0.997785i	$-0.521191\pi$
$953$	4.65385	−	0.669123i	0.150753	−	0.0216750i	0.217278	+	0.976110i	$0.430282\pi$
$954$	0.236772	+	0.168604i	0.00766577	+	0.00545877i
$955$	3.95679	−	41.4374i	0.128039	−	1.34088i
$956$	−14.1104	−	5.64895i	−0.456363	−	0.182700i
$957$	−0.992971	+	20.8450i	−0.0320982	+	0.673824i
$958$	1.54374	−	0.453283i	0.0498760	−	0.0146449i
$959$	−18.7965	−	42.2677i	−0.606971	−	1.36490i
$960$	10.4737	+	9.07553i	0.338038	+	0.292912i
$961$	−10.6819	−	5.50689i	−0.344577	−	0.177642i
$962$	5.25120	−	1.01209i	0.169306	−	0.0326310i
$963$	−12.6097	−	13.2247i	−0.406342	−	0.426159i
$964$	11.8637	−	1.13284i	0.382102	−	0.0364864i
$965$	19.2253			0.618886
$966$	0.825156	+	2.10083i	0.0265490	+	0.0675929i
$967$	51.8186			1.66637			0.833187	−	0.552992i	$-0.186514\pi$
$967$	51.8186			1.66637			0.833187	+	0.552992i	$0.186514\pi$
$968$	−0.470539	+	0.0449311i	−0.0151237	+	0.00144414i
$969$	32.1011	+	33.6666i	1.03123	+	1.08153i
$970$	−3.46393	+	0.667617i	−0.111220	+	0.0214359i
$971$	49.7018	+	25.6231i	1.59501	+	0.822283i	0.999825	+	0.0186924i	$0.00595033\pi$
$971$	49.7018	+	25.6231i	1.59501	+	0.822283i	0.595182	+	0.803591i	$0.297080\pi$
$972$	−1.48759	−	1.28900i	−0.0477143	−	0.0413447i
$973$	19.6882	−	27.0734i	0.631175	−	0.867934i
$974$	0.649835	−	0.190809i	0.0208221	−	0.00611391i
$975$	−0.226952	+	4.76430i	−0.00726827	+	0.152580i
$976$	7.17574	+	2.87273i	0.229690	+	0.0919540i
$977$	−3.02331	+	31.6616i	−0.0967243	+	1.01294i	0.808639	+	0.588305i	$0.200205\pi$
$977$	−3.02331	+	31.6616i	−0.0967243	+	1.01294i	−0.905363	+	0.424638i	$0.860401\pi$
$978$	−3.02634	−	2.15505i	−0.0967717	−	0.0689108i
$979$	17.9611	−	2.58242i	0.574041	−	0.0825346i
$980$	−0.728884	−	26.3261i	−0.0232833	−	0.840957i
$981$	−0.467076	−	1.59072i	−0.0149126	−	0.0507877i
$982$	2.43674	−	0.975523i	0.0777594	−	0.0311302i
$983$	15.1184	+	43.6817i	0.482201	+	1.39323i	0.879657	+	0.475608i	$0.157772\pi$
$983$	15.1184	+	43.6817i	0.482201	+	1.39323i	−0.397456	+	0.917621i	$0.630107\pi$
$984$	0.0712349	+	1.49540i	0.00227089	+	0.0476718i
$985$	1.15773	−	3.34504i	0.0368884	−	0.106582i
$986$	−6.37364	−	1.87147i	−0.202978	−	0.0595997i
$987$	6.14359	+	7.97441i	0.195553	+	0.253828i
$988$		−	56.3912i		−	1.79404i
$989$	−8.18543	+	58.3490i	−0.260281	+	1.85539i
$990$	−0.946392	−	0.546400i	−0.0300783	−	0.0173657i
$991$	−26.8477	−	37.7023i	−0.852844	−	1.19765i	−0.978637	−	0.205595i	$-0.934087\pi$
$991$	−26.8477	−	37.7023i	−0.852844	−	1.19765i	0.125793	−	0.992057i	$-0.459852\pi$
$992$	−8.84800	+	2.14650i	−0.280924	+	0.0681515i
$993$	−1.05065	+	0.910397i	−0.0333415	+	0.0288906i
$994$	−4.33485	+	3.02222i	−0.137493	+	0.0958590i
$995$	8.86825	−	10.2345i	0.281143	−	0.324456i
$996$	−11.1446	−	27.8379i	−0.353131	−	0.882078i
$997$	0.824693	+	0.200068i	0.0261183	+	0.00633623i	0.248797	−	0.968556i	$-0.419965\pi$
$997$	0.824693	+	0.200068i	0.0261183	+	0.00633623i	−0.222678	+	0.974892i	$0.571480\pi$
$998$	−1.17723	+	0.606906i	−0.0372647	+	0.0192113i
$999$	6.67167	−	5.24666i	0.211082	−	0.165997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bf.a.178.18	yes	640
7.5	odd	6	inner	483.2.bf.a.40.15	yes	640
23.19	odd	22	inner	483.2.bf.a.157.15	yes	640
161.19	even	66	inner	483.2.bf.a.19.18	✓	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bf.a.19.18	✓	640	161.19	even	66	inner
483.2.bf.a.40.15	yes	640	7.5	odd	6	inner
483.2.bf.a.157.15	yes	640	23.19	odd	22	inner
483.2.bf.a.178.18	yes	640	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.177076 - 0.0169087i) q^{2} +(-0.690079 - 0.723734i) q^{3} +(-1.93279 + 0.372514i) q^{4} +(1.69892 + 0.875853i) q^{5} +(-0.134434 - 0.116488i) q^{6} +(-2.13977 - 1.55608i) q^{7} +(-0.677305 + 0.198875i) q^{8} +(-0.0475819 + 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.177076 - 0.0169087i) q^{2} +(-0.690079 - 0.723734i) q^{3} +(-1.93279 + 0.372514i) q^{4} +(1.69892 + 0.875853i) q^{5} +(-0.134434 - 0.116488i) q^{6} +(-2.13977 - 1.55608i) q^{7} +(-0.677305 + 0.198875i) q^{8} +(-0.0475819 + 0.998867i) q^{9} +(0.315648 + 0.126366i) q^{10} +(-0.305519 + 3.19954i) q^{11} +(1.60338 + 1.14176i) q^{12} +(3.50608 - 0.504098i) q^{13} +(-0.405214 - 0.239363i) q^{14} +(-0.538503 - 1.83397i) q^{15} +(3.53815 - 1.41646i) q^{16} +(1.88112 + 5.43513i) q^{17} +(0.00846395 + 0.177680i) q^{18} +(-2.64533 + 7.64319i) q^{19} +(-3.60991 - 1.05997i) q^{20} +(0.350428 + 2.62244i) q^{21} +0.571728i q^{22} +(4.74465 - 0.698774i) q^{23} +(0.611326 + 0.352949i) q^{24} +(-0.781083 - 1.09688i) q^{25} +(0.612320 - 0.148547i) q^{26} +(0.755750 - 0.654861i) q^{27} +(4.71539 + 2.21047i) q^{28} +(-4.25192 + 4.90698i) q^{29} +(-0.126366 - 0.315648i) q^{30} +(-4.23404 - 1.02717i) q^{31} +(1.85743 - 0.957570i) q^{32} +(2.52645 - 1.98682i) q^{33} +(0.425003 + 0.930626i) q^{34} +(-2.27240 - 4.51777i) q^{35} +(-0.280127 - 1.94832i) q^{36} +(8.47795 + 0.403854i) q^{37} +(-0.339189 + 1.39816i) q^{38} +(-2.78430 - 2.18960i) q^{39} +(-1.32487 - 0.255348i) q^{40} +(1.14661 + 1.78417i) q^{41} +(0.106395 + 0.458447i) q^{42} +(-3.46130 + 11.7881i) q^{43} +(-0.601370 - 6.29784i) q^{44} +(-0.955698 + 1.65532i) q^{45} +(0.828350 - 0.203962i) q^{46} +(3.29504 - 1.90239i) q^{47} +(-3.46674 - 1.58321i) q^{48} +(2.15726 + 6.65930i) q^{49} +(-0.156858 - 0.181024i) q^{50} +(2.63547 - 5.11210i) q^{51} +(-6.58872 + 2.28038i) q^{52} +(1.01011 - 1.28445i) q^{53} +(0.122752 - 0.128739i) q^{54} +(-3.32138 + 5.16816i) q^{55} +(1.75874 + 0.628391i) q^{56} +(7.35713 - 3.35989i) q^{57} +(-0.669944 + 0.940805i) q^{58} +(2.71467 - 6.78093i) q^{59} +(1.72399 + 3.34408i) q^{60} +(1.46781 + 1.39955i) q^{61} +(-0.767116 - 0.110295i) q^{62} +(1.65613 - 2.06331i) q^{63} +(-6.09957 + 3.91996i) q^{64} +(6.39805 + 2.21439i) q^{65} +(0.413779 - 0.394538i) q^{66} +(-7.16923 + 5.10519i) q^{67} +(-5.66046 - 9.80421i) q^{68} +(-3.77991 - 2.95166i) q^{69} +(-0.478779 - 0.761566i) q^{70} +(4.66441 - 10.2136i) q^{71} +(-0.166422 - 0.686000i) q^{72} +(-0.886843 - 4.60138i) q^{73} +(1.50807 - 0.0718383i) q^{74} +(-0.254839 + 1.32223i) q^{75} +(2.26567 - 15.7581i) q^{76} +(5.63246 - 6.37088i) q^{77} +(-0.530057 - 0.340647i) q^{78} +(-2.97716 - 3.78577i) q^{79} +(7.25163 + 0.692447i) q^{80} +(-0.995472 - 0.0950560i) q^{81} +(0.233206 + 0.296546i) q^{82} +(-12.8156 - 8.23609i) q^{83} +(-1.65420 - 4.93808i) q^{84} +(-1.56451 + 10.8814i) q^{85} +(-0.413592 + 2.14592i) q^{86} +(6.48551 - 0.308943i) q^{87} +(-0.429377 - 2.22782i) q^{88} +(-1.33103 - 5.48657i) q^{89} +(-0.141242 + 0.309277i) q^{90} +(-8.28662 - 4.37707i) q^{91} +(-8.91010 + 3.11803i) q^{92} +(2.17843 + 3.77314i) q^{93} +(0.551307 - 0.392584i) q^{94} +(-11.1885 + 10.6682i) q^{95} +(-1.97480 - 0.683484i) q^{96} +(-8.72838 + 5.60939i) q^{97} +(0.494600 + 1.14273i) q^{98} +(-3.18138 - 0.457413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9}+O(q^{10}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9	\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99}+O(q^{100}) \) 640 * q - 4 * q^2 + 36 * q^4 + 24 * q^8 - 32 * q^9 + 4 * q^18 - 28 * q^23 + 56 * q^25 - 84 * q^26 - 176 * q^28 - 24 * q^29 + 12 * q^31 + 36 * q^32 - 76 * q^35 + 28 * q^36 + 44 * q^37 - 110 * q^42 - 88 * q^43 + 154 * q^44 + 8 * q^46 + 12 * q^47 - 8 * q^49 - 212 * q^50 + 44 * q^51 + 108 * q^52 - 110 * q^56 - 88 * q^57 + 2 * q^58 - 36 * q^59 - 168 * q^64 - 48 * q^70 + 16 * q^71 + 12 * q^72 - 48 * q^73 - 22 * q^74 + 48 * q^75 + 32 * q^78 - 44 * q^79 - 594 * q^80 + 32 * q^81 + 24 * q^82 + 352 * q^85 - 36 * q^87 - 330 * q^88 + 244 * q^92 - 24 * q^93 - 486 * q^94 - 154 * q^95 - 60 * q^96 - 24 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more